Adaptive random walks on the class of Web graphs

Science.gov (United States)

Tadić, B.

2001-09-01

We study random walk with adaptive move strategies on a class of directed graphs with variable wiring diagram. The graphs are grown from the evolution rules compatible with the dynamics of the world-wide Web [B. Tadić, Physica A 293, 273 (2001)], and are characterized by a pair of power-law distributions of out- and in-degree for each value of the parameter β, which measures the degree of rewiring in the graph. The walker adapts its move strategy according to locally available information both on out-degree of the visited node and in-degree of target node. A standard random walk, on the other hand, uses the out-degree only. We compute the distribution of connected subgraphs visited by an ensemble of walkers, the average access time and survival probability of the walks. We discuss these properties of the walk dynamics relative to the changes in the global graph structure when the control parameter β is varied. For β≥ 3, corresponding to the world-wide Web, the access time of the walk to a given level of hierarchy on the graph is much shorter compared to the standard random walk on the same graph. By reducing the amount of rewiring towards rigidity limit β↦βc≲ 0.1, corresponding to the range of naturally occurring biochemical networks, the survival probability of adaptive and standard random walk become increasingly similar. The adaptive random walk can be used as an efficient message-passing algorithm on this class of graphs for large degree of rewiring.

Replica methods for loopy sparse random graphs

International Nuclear Information System (INIS)

Coolen, ACC

2016-01-01

I report on the development of a novel statistical mechanical formalism for the analysis of random graphs with many short loops, and processes on such graphs. The graphs are defined via maximum entropy ensembles, in which both the degrees (via hard constraints) and the adjacency matrix spectrum (via a soft constraint) are prescribed. The sum over graphs can be done analytically, using a replica formalism with complex replica dimensions. All known results for tree-like graphs are recovered in a suitable limit. For loopy graphs, the emerging theory has an appealing and intuitive structure, suggests how message passing algorithms should be adapted, and what is the structure of theories describing spin systems on loopy architectures. However, the formalism is still largely untested, and may require further adjustment and refinement. (paper)

Aspects of random geometric graphs : Pursuit-evasion and treewidth

NARCIS (Netherlands)

Li, A.

2015-01-01

In this thesis, we studied two aspects of random geometric graphs: pursuit-evasion and treewidth. We first studied one pursuit-evasion game: Cops and Robbers. This game, which dates back to 1970s, are studied extensively in recent years. We investigate this game on random geometric graphs, and get

Cross over of recurrence networks to random graphs and random ...

Indian Academy of Sciences (India)

2017-01-27

Jan 27, 2017 ... that all recurrence networks can cross over to random geometric graphs by adding sufficient amount of noise to .... municative [19] or social [20], deviate from the random ..... He has shown that the spatial effects become.

First-passage percolation on the random graph

NARCIS (Netherlands)

Hofstad, van der R.W.; Hooghiemstra, G.; Van Mieghem, P.

2001-01-01

We study first-passage percolation on the random graph Gp(N) with exponentially distributed weights on the links. For the special case of the complete graph, this problem can be described in terms of a continuous-time Markov chain and recursive trees. The Markov chain X(t) describes the number of

Evolution of a Modified Binomial Random Graph by Agglomeration

Science.gov (United States)

Kang, Mihyun; Pachon, Angelica; Rodríguez, Pablo M.

2018-02-01

In the classical Erdős-Rényi random graph G( n, p) there are n vertices and each of the possible edges is independently present with probability p. The random graph G( n, p) is homogeneous in the sense that all vertices have the same characteristics. On the other hand, numerous real-world networks are inhomogeneous in this respect. Such an inhomogeneity of vertices may influence the connection probability between pairs of vertices. The purpose of this paper is to propose a new inhomogeneous random graph model which is obtained in a constructive way from the Erdős-Rényi random graph G( n, p). Given a configuration of n vertices arranged in N subsets of vertices (we call each subset a super-vertex), we define a random graph with N super-vertices by letting two super-vertices be connected if and only if there is at least one edge between them in G( n, p). Our main result concerns the threshold for connectedness. We also analyze the phase transition for the emergence of the giant component and the degree distribution. Even though our model begins with G( n, p), it assumes the existence of some community structure encoded in the configuration. Furthermore, under certain conditions it exhibits a power law degree distribution. Both properties are important for real-world applications.

Groups, graphs and random walks

CERN Document Server

Salvatori, Maura; Sava-Huss, Ecaterina

2017-01-01

An accessible and panoramic account of the theory of random walks on groups and graphs, stressing the strong connections of the theory with other branches of mathematics, including geometric and combinatorial group theory, potential analysis, and theoretical computer science. This volume brings together original surveys and research-expository papers from renowned and leading experts, many of whom spoke at the workshop 'Groups, Graphs and Random Walks' celebrating the sixtieth birthday of Wolfgang Woess in Cortona, Italy. Topics include: growth and amenability of groups; Schrödinger operators and symbolic dynamics; ergodic theorems; Thompson's group F; Poisson boundaries; probability theory on buildings and groups of Lie type; structure trees for edge cuts in networks; and mathematical crystallography. In what is currently a fast-growing area of mathematics, this book provides an up-to-date and valuable reference for both researchers and graduate students, from which future research activities will undoubted...

The hard-core model on random graphs revisited

International Nuclear Information System (INIS)

Barbier, Jean; Krzakala, Florent; Zhang, Pan; Zdeborová, Lenka

2013-01-01

We revisit the classical hard-core model, also known as independent set and dual to vertex cover problem, where one puts particles with a first-neighbor hard-core repulsion on the vertices of a random graph. Although the case of random graphs with small and very large average degrees respectively are quite well understood, they yield qualitatively different results and our aim here is to reconciliate these two cases. We revisit results that can be obtained using the (heuristic) cavity method and show that it provides a closed-form conjecture for the exact density of the densest packing on random regular graphs with degree K ≥ 20, and that for K > 16 the nature of the phase transition is the same as for large K. This also shows that the hard-code model is the simplest mean-field lattice model for structural glasses and jamming

On the number of subgraphs of the Barabasi-Albert random graph

Energy Technology Data Exchange (ETDEWEB)

Ryabchenko, Aleksandr A; Samosvat, Egor A [Moscow Institute of Physics and Technology (State University), Dolgoprudnyi, Moscow Region, Russian Frderation (Russian Federation)

2012-06-30

We study a model of a random graph of the type of the Barabasi-Albert preferential attachment model. We develop a technique that makes it possible to estimate the mathematical expectation for a fairly wide class of random variables in the model under consideration. We use this technique to prove a theorem on the asymptotics of the mathematical expectation of the number of subgraphs isomorphic to a certain fixed graph in the random graphs of this model.

Infinite Random Graphs as Statistical Mechanical Models

DEFF Research Database (Denmark)

Durhuus, Bergfinnur Jøgvan; Napolitano, George Maria

2011-01-01

We discuss two examples of infinite random graphs obtained as limits of finite statistical mechanical systems: a model of two-dimensional dis-cretized quantum gravity defined in terms of causal triangulated surfaces, and the Ising model on generic random trees. For the former model we describe a ...

Recent developments in exponential random graph (p*) models for social networks

NARCIS (Netherlands)

Robins, Garry; Snijders, Tom; Wang, Peng; Handcock, Mark; Pattison, Philippa

This article reviews new specifications for exponential random graph models proposed by Snijders et al. [Snijders, T.A.B., Pattison, P., Robins, G.L., Handcock, M., 2006. New specifications for exponential random graph models. Sociological Methodology] and demonstrates their improvement over

On the Distribution of Random Geometric Graphs

DEFF Research Database (Denmark)

Badiu, Mihai Alin; Coon, Justin P.

2018-01-01

as a measure of the graph’s topological uncertainty (or information content). Moreover, the distribution is also relevant for determining average network performance or designing protocols. However, a major impediment in deducing the graph distribution is that it requires the joint probability distribution......Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the underlying spatial embedding. We concern ourselves with the probability distribution of an RGG, which is crucial for studying its random topology, properties (e.g., connectedness), or Shannon entropy...... of the n(n − 1)/2 distances between n nodes randomly distributed in a bounded domain. As no such result exists in the literature, we make progress by obtaining the joint distribution of the distances between three nodes confined in a disk in R 2. This enables the calculation of the probability distribution...

Probability on graphs random processes on graphs and lattices

CERN Document Server

Grimmett, Geoffrey

2018-01-01

This introduction to some of the principal models in the theory of disordered systems leads the reader through the basics, to the very edge of contemporary research, with the minimum of technical fuss. Topics covered include random walk, percolation, self-avoiding walk, interacting particle systems, uniform spanning tree, random graphs, as well as the Ising, Potts, and random-cluster models for ferromagnetism, and the Lorentz model for motion in a random medium. This new edition features accounts of major recent progress, including the exact value of the connective constant of the hexagonal lattice, and the critical point of the random-cluster model on the square lattice. The choice of topics is strongly motivated by modern applications, and focuses on areas that merit further research. Accessible to a wide audience of mathematicians and physicists, this book can be used as a graduate course text. Each chapter ends with a range of exercises.

A weak zero-one law for sequences of random distance graphs

Energy Technology Data Exchange (ETDEWEB)

Zhukovskii, Maksim E [M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)

2012-07-31

We study zero-one laws for properties of random distance graphs. Properties written in a first-order language are considered. For p(N) such that pN{sup {alpha}}{yields}{infinity} as N{yields}{infinity}, and (1-p)N{sup {alpha}} {yields} {infinity} as N {yields} {infinity} for any {alpha}>0, we succeed in refuting the law. In this connection, we consider a weak zero-one j-law. For this law, we obtain results for random distance graphs which are similar to the assertions concerning the classical zero-one law for random graphs. Bibliography: 18 titles.

A cluster expansion approach to exponential random graph models

International Nuclear Information System (INIS)

Yin, Mei

2012-01-01

The exponential family of random graphs are among the most widely studied network models. We show that any exponential random graph model may alternatively be viewed as a lattice gas model with a finite Banach space norm. The system may then be treated using cluster expansion methods from statistical mechanics. In particular, we derive a convergent power series expansion for the limiting free energy in the case of small parameters. Since the free energy is the generating function for the expectations of other random variables, this characterizes the structure and behavior of the limiting network in this parameter region

Critical behavior in inhomogeneous random graphs

NARCIS (Netherlands)

Hofstad, van der R.W.

2009-01-01

We study the critical behavior of inhomogeneous random graphs where edges are present independently but with unequal edge occupation probabilities. We show that the critical behavior depends sensitively on the properties of the asymptotic degrees. Indeed, when the proportion of vertices with degree

Cluster Tails for Critical Power-Law Inhomogeneous Random Graphs

Science.gov (United States)

van der Hofstad, Remco; Kliem, Sandra; van Leeuwaarden, Johan S. H.

2018-04-01

Recently, the scaling limit of cluster sizes for critical inhomogeneous random graphs of rank-1 type having finite variance but infinite third moment degrees was obtained in Bhamidi et al. (Ann Probab 40:2299-2361, 2012). It was proved that when the degrees obey a power law with exponent τ \\in (3,4), the sequence of clusters ordered in decreasing size and multiplied through by n^{-(τ -2)/(τ -1)} converges as n→ ∞ to a sequence of decreasing non-degenerate random variables. Here, we study the tails of the limit of the rescaled largest cluster, i.e., the probability that the scaling limit of the largest cluster takes a large value u, as a function of u. This extends a related result of Pittel (J Combin Theory Ser B 82(2):237-269, 2001) for the Erdős-Rényi random graph to the setting of rank-1 inhomogeneous random graphs with infinite third moment degrees. We make use of delicate large deviations and weak convergence arguments.

Random Walks and Diffusions on Graphs and Databases An Introduction

CERN Document Server

Blanchard, Philippe

2011-01-01

Most networks and databases that humans have to deal with contain large, albeit finite number of units. Their structure, for maintaining functional consistency of the components, is essentially not random and calls for a precise quantitative description of relations between nodes (or data units) and all network components. This book is an introduction, for both graduate students and newcomers to the field, to the theory of graphs and random walks on such graphs. The methods based on random walks and diffusions for exploring the structure of finite connected graphs and databases are reviewed (Markov chain analysis). This provides the necessary basis for consistently discussing a number of applications such diverse as electric resistance networks, estimation of land prices, urban planning, linguistic databases, music, and gene expression regulatory networks.

Formation of Robust Multi-Agent Networks through Self-Organizing Random Regular Graphs

KAUST Repository

Yasin Yazicioǧlu, A.; Egerstedt, Magnus; Shamma, Jeff S.

2015-01-01

Multi-Agent networks are often modeled as interaction graphs, where the nodes represent the agents and the edges denote some direct interactions. The robustness of a multi-Agent network to perturbations such as failures, noise, or malicious attacks largely depends on the corresponding graph. In many applications, networks are desired to have well-connected interaction graphs with relatively small number of links. One family of such graphs is the random regular graphs. In this paper, we present a decentralized scheme for transforming any connected interaction graph with a possibly non-integer average degree of k into a connected random m-regular graph for some m ϵ [k+k ] 2. Accordingly, the agents improve the robustness of the network while maintaining a similar number of links as the initial configuration by locally adding or removing some edges. © 2015 IEEE.

Formation of Robust Multi-Agent Networks through Self-Organizing Random Regular Graphs

KAUST Repository

Yasin Yazicioǧlu, A.

2015-11-25

Multi-Agent networks are often modeled as interaction graphs, where the nodes represent the agents and the edges denote some direct interactions. The robustness of a multi-Agent network to perturbations such as failures, noise, or malicious attacks largely depends on the corresponding graph. In many applications, networks are desired to have well-connected interaction graphs with relatively small number of links. One family of such graphs is the random regular graphs. In this paper, we present a decentralized scheme for transforming any connected interaction graph with a possibly non-integer average degree of k into a connected random m-regular graph for some m ϵ [k+k ] 2. Accordingly, the agents improve the robustness of the network while maintaining a similar number of links as the initial configuration by locally adding or removing some edges. © 2015 IEEE.

Critical behavior in inhomogeneous random graphs

NARCIS (Netherlands)

Hofstad, van der R.W.

2013-01-01

We study the critical behavior of inhomogeneous random graphs in the so-called rank-1 case, where edges are present independently but with unequal edge occupation probabilities. The edge occupation probabilities are moderated by vertex weights, and are such that the degree of vertex i is close in

On the number of subgraphs of the Barabási-Albert random graph

International Nuclear Information System (INIS)

Ryabchenko, Aleksandr A; Samosvat, Egor A

2012-01-01

We study a model of a random graph of the type of the Barabási-Albert preferential attachment model. We develop a technique that makes it possible to estimate the mathematical expectation for a fairly wide class of random variables in the model under consideration. We use this technique to prove a theorem on the asymptotics of the mathematical expectation of the number of subgraphs isomorphic to a certain fixed graph in the random graphs of this model.

Transduction on Directed Graphs via Absorbing Random Walks.

Science.gov (United States)

De, Jaydeep; Zhang, Xiaowei; Lin, Feng; Cheng, Li

2017-08-11

In this paper we consider the problem of graph-based transductive classification, and we are particularly interested in the directed graph scenario which is a natural form for many real world applications.Different from existing research efforts that either only deal with undirected graphs or circumvent directionality by means of symmetrization, we propose a novel random walk approach on directed graphs using absorbing Markov chains, which can be regarded as maximizing the accumulated expected number of visits from the unlabeled transient states. Our algorithm is simple, easy to implement, and works with large-scale graphs on binary, multiclass, and multi-label prediction problems. Moreover, it is capable of preserving the graph structure even when the input graph is sparse and changes over time, as well as retaining weak signals presented in the directed edges. We present its intimate connections to a number of existing methods, including graph kernels, graph Laplacian based methods, and interestingly, spanning forest of graphs. Its computational complexity and the generalization error are also studied. Empirically our algorithm is systematically evaluated on a wide range of applications, where it has shown to perform competitively comparing to a suite of state-of-the-art methods. In particular, our algorithm is shown to work exceptionally well with large sparse directed graphs with e.g. millions of nodes and tens of millions of edges, where it significantly outperforms other state-of-the-art methods. In the dynamic graph setting involving insertion or deletion of nodes and edge-weight changes over time, it also allows efficient online updates that produce the same results as of the batch update counterparts.

Bridging Weighted Rules and Graph Random Walks for Statistical Relational Models

Directory of Open Access Journals (Sweden)

Seyed Mehran Kazemi

2018-02-01

Full Text Available The aim of statistical relational learning is to learn statistical models from relational or graph-structured data. Three main statistical relational learning paradigms include weighted rule learning, random walks on graphs, and tensor factorization. These paradigms have been mostly developed and studied in isolation for many years, with few works attempting at understanding the relationship among them or combining them. In this article, we study the relationship between the path ranking algorithm (PRA, one of the most well-known relational learning methods in the graph random walk paradigm, and relational logistic regression (RLR, one of the recent developments in weighted rule learning. We provide a simple way to normalize relations and prove that relational logistic regression using normalized relations generalizes the path ranking algorithm. This result provides a better understanding of relational learning, especially for the weighted rule learning and graph random walk paradigms. It opens up the possibility of using the more flexible RLR rules within PRA models and even generalizing both by including normalized and unnormalized relations in the same model.

Large Deviations for the Annealed Ising Model on Inhomogeneous Random Graphs: Spins and Degrees

Science.gov (United States)

Dommers, Sander; Giardinà, Cristian; Giberti, Claudio; Hofstad, Remco van der

2018-04-01

We prove a large deviations principle for the total spin and the number of edges under the annealed Ising measure on generalized random graphs. We also give detailed results on how the annealing over the Ising model changes the degrees of the vertices in the graph and show how it gives rise to interesting correlated random graphs.

Continuous-Time Classical and Quantum Random Walk on Direct Product of Cayley Graphs

International Nuclear Information System (INIS)

Salimi, S.; Jafarizadeh, M. A.

2009-01-01

In this paper we define direct product of graphs and give a recipe for obtaining probability of observing particle on vertices in the continuous-time classical and quantum random walk. In the recipe, the probability of observing particle on direct product of graph is obtained by multiplication of probability on the corresponding to sub-graphs, where this method is useful to determining probability of walk on complicated graphs. Using this method, we calculate the probability of continuous-time classical and quantum random walks on many of finite direct product Cayley graphs (complete cycle, complete K n , charter and n-cube). Also, we inquire that the classical state the stationary uniform distribution is reached as t → ∞ but for quantum state is not always satisfied. (general)

Greedy Local Search and Vertex Cover in Sparse Random Graphs

DEFF Research Database (Denmark)

Witt, Carsten

2009-01-01

. This work starts with a rigorous explanation for this claim based on the refined analysis of the Karp-Sipser algorithm by Aronson et al. Subsequently, theoretical supplements are given to experimental studies of search heuristics on random graphs. For c 1, a greedy and randomized local-search heuristic...... finds an optimal cover in polynomial time with a probability arbitrarily close to 1. This behavior relies on the absence of a giant component. As an additional insight into the randomized search, it is shown that the heuristic fails badly also on graphs consisting of a single tree component of maximum......Recently, various randomized search heuristics have been studied for the solution of the minimum vertex cover problem, in particular for sparse random instances according to the G(n, c/n) model, where c > 0 is a constant. Methods from statistical physics suggest that the problem is easy if c

Cliques in dense inhomogenous random graphs

Czech Academy of Sciences Publication Activity Database

Doležal, Martin; Hladký, Jan; Máthé, A.

2017-01-01

Roč. 51, č. 2 (2017), s. 275-314 ISSN 1042-9832 R&D Projects: GA ČR GA16-07378S EU Projects: European Commission(XE) 628974 - PAECIDM Institutional support: RVO:67985840 Keywords : inhomogeneous random graphs * clique number Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.243, year: 2016 http://onlinelibrary.wiley.com/doi/10.1002/ rsa .20715/abstract

Cliques in dense inhomogenous random graphs

Czech Academy of Sciences Publication Activity Database

Doležal, Martin; Hladký, Jan; Máthé, A.

2017-01-01

Roč. 51, č. 2 (2017), s. 275-314 ISSN 1042-9832 R&D Projects: GA ČR GA16-07378S EU Projects: European Commission(XE) 628974 - PAECIDM Institutional support: RVO:67985840 Keywords : inhomogeneous random graphs * clique number Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.243, year: 2016 http://onlinelibrary.wiley.com/doi/10.1002/rsa.20715/abstract

A Study on the Amount of Random Graph Groupies

OpenAIRE

Lu, Daodi

2013-01-01

In 1980, Ajtai, Komlos and Szemer{\\'e}di defined "groupie": Let $G=(V,E)$ be a simple graph, $|V|=n$, $|E|=e$. For a vertex $v\\in V$, let $r(v)$ denote the sum of the degrees of the vertices adjacent to $v$. We say $v\\in V$ is a {\\it groupie}, if $\\frac{r(v)}{\\deg(v)}\\geq\\frac{e}{n}.$ In this paper, we prove that in random graph $B(n,p)$, $0

PageRank in scale-free random graphs

NARCIS (Netherlands)

Chen, Ningyuan; Litvak, Nelli; Olvera-Cravioto, Mariana; Bonata, Anthony; Chung, Fan; Pralat, Paweł

2014-01-01

We analyze the distribution of PageRank on a directed configuration model and show that as the size of the graph grows to infinity, the PageRank of a randomly chosen node can be closely approximated by the PageRank of the root node of an appropriately constructed tree. This tree approximation is in

Personalized PageRank Clustering: A graph clustering algorithm based on random walks

Science.gov (United States)

A. Tabrizi, Shayan; Shakery, Azadeh; Asadpour, Masoud; Abbasi, Maziar; Tavallaie, Mohammad Ali

2013-11-01

Graph clustering has been an essential part in many methods and thus its accuracy has a significant effect on many applications. In addition, exponential growth of real-world graphs such as social networks, biological networks and electrical circuits demands clustering algorithms with nearly-linear time and space complexity. In this paper we propose Personalized PageRank Clustering (PPC) that employs the inherent cluster exploratory property of random walks to reveal the clusters of a given graph. We combine random walks and modularity to precisely and efficiently reveal the clusters of a graph. PPC is a top-down algorithm so it can reveal inherent clusters of a graph more accurately than other nearly-linear approaches that are mainly bottom-up. It also gives a hierarchy of clusters that is useful in many applications. PPC has a linear time and space complexity and has been superior to most of the available clustering algorithms on many datasets. Furthermore, its top-down approach makes it a flexible solution for clustering problems with different requirements.

The Canopy Graph and Level Statistics for Random Operators on Trees

International Nuclear Information System (INIS)

Aizenman, Michael; Warzel, Simone

2006-01-01

For operators with homogeneous disorder, it is generally expected that there is a relation between the spectral characteristics of a random operator in the infinite setup and the distribution of the energy gaps in its finite volume versions, in corresponding energy ranges. Whereas pure point spectrum of the infinite operator goes along with Poisson level statistics, it is expected that purely absolutely continuous spectrum would be associated with gap distributions resembling the corresponding random matrix ensemble. We prove that on regular rooted trees, which exhibit both spectral types, the eigenstate point process has always Poissonian limit. However, we also find that this does not contradict the picture described above if that is carefully interpreted, as the relevant limit of finite trees is not the infinite homogenous tree graph but rather a single-ended 'canopy graph.' For this tree graph, the random Schroedinger operator is proven here to have only pure-point spectrum at any strength of the disorder. For more general single-ended trees it is shown that the spectrum is always singular - pure point possibly with singular continuous component which is proven to occur in some cases

Random geometric graphs with general connection functions

Science.gov (United States)

Dettmann, Carl P.; Georgiou, Orestis

2016-03-01

In the original (1961) Gilbert model of random geometric graphs, nodes are placed according to a Poisson point process, and links formed between those within a fixed range. Motivated by wireless ad hoc networks "soft" or "probabilistic" connection models have recently been introduced, involving a "connection function" H (r ) that gives the probability that two nodes at distance r are linked (directly connect). In many applications (not only wireless networks), it is desirable that the graph is connected; that is, every node is linked to every other node in a multihop fashion. Here the connection probability of a dense network in a convex domain in two or three dimensions is expressed in terms of contributions from boundary components for a very general class of connection functions. It turns out that only a few quantities such as moments of the connection function appear. Good agreement is found with special cases from previous studies and with numerical simulations.

Cluster tails for critical power-law inhomogeneous random graphs

NARCIS (Netherlands)

van der Hofstad, R.; Kliem, S.; van Leeuwaarden, J.S.H.

2018-01-01

Recently, the scaling limit of cluster sizes for critical inhomogeneous random graphs of rank-1 type having finite variance but infinite third moment degrees was obtained in Bhamidi et al. (Ann Probab 40:2299–2361, 2012). It was proved that when the degrees obey a power law with exponent τ∈ (3 , 4)

Long range order and giant components of quantum random graphs

CERN Document Server

Ioffe, D

2006-01-01

Mean field quantum random graphs give a natural generalization of classical Erd\\H{o}s-R\\'{e}nyi percolation model on complete graph $G_N$ with $p =\\beta /N$. Quantum case incorporates an additional parameter $\\lambda\\geq 0$, and the short-long range order transition should be studied in the $(\\beta ,\\lambda)$-quarter plane. In this work we explicitly compute the corresponding critical curve $\\gamma_c$, and derive results on two-point functions and sizes of connected components in both short and long range order regions. In this way the classical case corresponds to the limiting point $(\\beta_c ,0) = (1,0)$ on $\\gamma_c$.

Investigating Facebook Groups through a Random Graph Model

OpenAIRE

Dinithi Pallegedara; Lei Pan

2014-01-01

Facebook disseminates messages for billions of users everyday. Though there are log files stored on central servers, law enforcement agencies outside of the U.S. cannot easily acquire server log files from Facebook. This work models Facebook user groups by using a random graph model. Our aim is to facilitate detectives quickly estimating the size of a Facebook group with which a suspect is involved. We estimate this group size according to the number of immediate friends and the number of ext...

On the number of spanning trees in random regular graphs

DEFF Research Database (Denmark)

Greenhill, Catherine; Kwan, Matthew; Wind, David Kofoed

2014-01-01

Let d >= 3 be a fixed integer. We give an asympotic formula for the expected number of spanning trees in a uniformly random d-regular graph with n vertices. (The asymptotics are as n -> infinity, restricted to even n if d is odd.) We also obtain the asymptotic distribution of the number of spanning...

Bayesian analysis for exponential random graph models using the adaptive exchange sampler

KAUST Repository

Jin, Ick Hoon; Liang, Faming; Yuan, Ying

2013-01-01

Exponential random graph models have been widely used in social network analysis. However, these models are extremely difficult to handle from a statistical viewpoint, because of the existence of intractable normalizing constants. In this paper, we

P2 : A random effects model with covariates for directed graphs

NARCIS (Netherlands)

van Duijn, M.A.J.; Snijders, T.A.B.; Zijlstra, B.J.H.

A random effects model is proposed for the analysis of binary dyadic data that represent a social network or directed graph, using nodal and/or dyadic attributes as covariates. The network structure is reflected by modeling the dependence between the relations to and from the same actor or node.

Exponential random graph models for networks with community structure.

Science.gov (United States)

Fronczak, Piotr; Fronczak, Agata; Bujok, Maksymilian

2013-09-01

Although the community structure organization is an important characteristic of real-world networks, most of the traditional network models fail to reproduce the feature. Therefore, the models are useless as benchmark graphs for testing community detection algorithms. They are also inadequate to predict various properties of real networks. With this paper we intend to fill the gap. We develop an exponential random graph approach to networks with community structure. To this end we mainly built upon the idea of blockmodels. We consider both the classical blockmodel and its degree-corrected counterpart and study many of their properties analytically. We show that in the degree-corrected blockmodel, node degrees display an interesting scaling property, which is reminiscent of what is observed in real-world fractal networks. A short description of Monte Carlo simulations of the models is also given in the hope of being useful to others working in the field.

Bond percolation on a class of correlated and clustered random graphs

International Nuclear Information System (INIS)

Allard, A; Hébert-Dufresne, L; Noël, P-A; Marceau, V; Dubé, L J

2012-01-01

We introduce a formalism for computing bond percolation properties of a class of correlated and clustered random graphs. This class of graphs is a generalization of the configuration model where nodes of different types are connected via different types of hyperedges, edges that can link more than two nodes. We argue that the multitype approach coupled with the use of clustered hyperedges can reproduce a wide spectrum of complex patterns, and thus enhances our capability to model real complex networks. As an illustration of this claim, we use our formalism to highlight unusual behaviours of the size and composition of the components (small and giant) in a synthetic, albeit realistic, social network. (paper)

Learning of Multimodal Representations With Random Walks on the Click Graph.

Science.gov (United States)

Wu, Fei; Lu, Xinyan; Song, Jun; Yan, Shuicheng; Zhang, Zhongfei Mark; Rui, Yong; Zhuang, Yueting

2016-02-01

In multimedia information retrieval, most classic approaches tend to represent different modalities of media in the same feature space. With the click data collected from the users' searching behavior, existing approaches take either one-to-one paired data (text-image pairs) or ranking examples (text-query-image and/or image-query-text ranking lists) as training examples, which do not make full use of the click data, particularly the implicit connections among the data objects. In this paper, we treat the click data as a large click graph, in which vertices are images/text queries and edges indicate the clicks between an image and a query. We consider learning a multimodal representation from the perspective of encoding the explicit/implicit relevance relationship between the vertices in the click graph. By minimizing both the truncated random walk loss as well as the distance between the learned representation of vertices and their corresponding deep neural network output, the proposed model which is named multimodal random walk neural network (MRW-NN) can be applied to not only learn robust representation of the existing multimodal data in the click graph, but also deal with the unseen queries and images to support cross-modal retrieval. We evaluate the latent representation learned by MRW-NN on a public large-scale click log data set Clickture and further show that MRW-NN achieves much better cross-modal retrieval performance on the unseen queries/images than the other state-of-the-art methods.

Exact two-point resistance, and the simple random walk on the complete graph minus N edges

International Nuclear Information System (INIS)

Chair, Noureddine

2012-01-01

An analytical approach is developed to obtain the exact expressions for the two-point resistance and the total effective resistance of the complete graph minus N edges of the opposite vertices. These expressions are written in terms of certain numbers that we introduce, which we call the Bejaia and the Pisa numbers; these numbers are the natural generalizations of the bisected Fibonacci and Lucas numbers. The correspondence between random walks and the resistor networks is then used to obtain the exact expressions for the first passage and mean first passage times on this graph. - Highlights: ► We obtain exact formulas for the two-point resistance of the complete graph minus N edges. ► We obtain also the total effective resistance of this graph. ► We modified Schwatt’s formula on trigonometrical power sum to suit our computations. ► We introduced the generalized bisected Fibonacci and Lucas numbers: the Bejaia and the Pisa numbers. ► The first passage and mean first passage times of the random walks have exact expressions.

Bayesian analysis for exponential random graph models using the adaptive exchange sampler

KAUST Repository

Jin, Ick Hoon

2013-01-01

Exponential random graph models have been widely used in social network analysis. However, these models are extremely difficult to handle from a statistical viewpoint, because of the existence of intractable normalizing constants. In this paper, we consider a fully Bayesian analysis for exponential random graph models using the adaptive exchange sampler, which solves the issue of intractable normalizing constants encountered in Markov chain Monte Carlo (MCMC) simulations. The adaptive exchange sampler can be viewed as a MCMC extension of the exchange algorithm, and it generates auxiliary networks via an importance sampling procedure from an auxiliary Markov chain running in parallel. The convergence of this algorithm is established under mild conditions. The adaptive exchange sampler is illustrated using a few social networks, including the Florentine business network, molecule synthetic network, and dolphins network. The results indicate that the adaptive exchange algorithm can produce more accurate estimates than approximate exchange algorithms, while maintaining the same computational efficiency.

Using Graph and Vertex Entropy to Compare Empirical Graphs with Theoretical Graph Models

Directory of Open Access Journals (Sweden)

Tomasz Kajdanowicz

2016-09-01

Full Text Available Over the years, several theoretical graph generation models have been proposed. Among the most prominent are: the Erdős–Renyi random graph model, Watts–Strogatz small world model, Albert–Barabási preferential attachment model, Price citation model, and many more. Often, researchers working with real-world data are interested in understanding the generative phenomena underlying their empirical graphs. They want to know which of the theoretical graph generation models would most probably generate a particular empirical graph. In other words, they expect some similarity assessment between the empirical graph and graphs artificially created from theoretical graph generation models. Usually, in order to assess the similarity of two graphs, centrality measure distributions are compared. For a theoretical graph model this means comparing the empirical graph to a single realization of a theoretical graph model, where the realization is generated from the given model using an arbitrary set of parameters. The similarity between centrality measure distributions can be measured using standard statistical tests, e.g., the Kolmogorov–Smirnov test of distances between cumulative distributions. However, this approach is both error-prone and leads to incorrect conclusions, as we show in our experiments. Therefore, we propose a new method for graph comparison and type classification by comparing the entropies of centrality measure distributions (degree centrality, betweenness centrality, closeness centrality. We demonstrate that our approach can help assign the empirical graph to the most similar theoretical model using a simple unsupervised learning method.

Degree distributions of the visibility graphs mapped from fractional Brownian motions and multifractal random walks

International Nuclear Information System (INIS)

Ni Xiaohui; Jiang Zhiqiang; Zhou Weixing

2009-01-01

The dynamics of a complex system is usually recorded in the form of time series, which can be studied through its visibility graph from a complex network perspective. We investigate the visibility graphs extracted from fractional Brownian motions and multifractal random walks, and find that the degree distributions exhibit power-law behaviors, in which the power-law exponent α is a linear function of the Hurst index H of the time series. We also find that the degree distribution of the visibility graph is mainly determined by the temporal correlation of the original time series with minor influence from the possible multifractal nature. As an example, we study the visibility graphs constructed from three Chinese stock market indexes and unveil that the degree distributions have power-law tails, where the tail exponents of the visibility graphs and the Hurst indexes of the indexes are close to the α∼H linear relationship.

Exact two-point resistance, and the simple random walk on the complete graph minus N edges

Energy Technology Data Exchange (ETDEWEB)

Chair, Noureddine, E-mail: n.chair@ju.edu.jo

2012-12-15

An analytical approach is developed to obtain the exact expressions for the two-point resistance and the total effective resistance of the complete graph minus N edges of the opposite vertices. These expressions are written in terms of certain numbers that we introduce, which we call the Bejaia and the Pisa numbers; these numbers are the natural generalizations of the bisected Fibonacci and Lucas numbers. The correspondence between random walks and the resistor networks is then used to obtain the exact expressions for the first passage and mean first passage times on this graph. - Highlights: Black-Right-Pointing-Pointer We obtain exact formulas for the two-point resistance of the complete graph minus N edges. Black-Right-Pointing-Pointer We obtain also the total effective resistance of this graph. Black-Right-Pointing-Pointer We modified Schwatt's formula on trigonometrical power sum to suit our computations. Black-Right-Pointing-Pointer We introduced the generalized bisected Fibonacci and Lucas numbers: the Bejaia and the Pisa numbers. Black-Right-Pointing-Pointer The first passage and mean first passage times of the random walks have exact expressions.

CONSISTENCY UNDER SAMPLING OF EXPONENTIAL RANDOM GRAPH MODELS.

Science.gov (United States)

Shalizi, Cosma Rohilla; Rinaldo, Alessandro

2013-04-01

The growing availability of network data and of scientific interest in distributed systems has led to the rapid development of statistical models of network structure. Typically, however, these are models for the entire network, while the data consists only of a sampled sub-network. Parameters for the whole network, which is what is of interest, are estimated by applying the model to the sub-network. This assumes that the model is consistent under sampling , or, in terms of the theory of stochastic processes, that it defines a projective family. Focusing on the popular class of exponential random graph models (ERGMs), we show that this apparently trivial condition is in fact violated by many popular and scientifically appealing models, and that satisfying it drastically limits ERGM's expressive power. These results are actually special cases of more general results about exponential families of dependent random variables, which we also prove. Using such results, we offer easily checked conditions for the consistency of maximum likelihood estimation in ERGMs, and discuss some possible constructive responses.

Quantitative graph theory mathematical foundations and applications

CERN Document Server

Dehmer, Matthias

2014-01-01

The first book devoted exclusively to quantitative graph theory, Quantitative Graph Theory: Mathematical Foundations and Applications presents and demonstrates existing and novel methods for analyzing graphs quantitatively. Incorporating interdisciplinary knowledge from graph theory, information theory, measurement theory, and statistical techniques, this book covers a wide range of quantitative-graph theoretical concepts and methods, including those pertaining to real and random graphs such as:Comparative approaches (graph similarity or distance)Graph measures to characterize graphs quantitat

Dynamical replica analysis of processes on finitely connected random graphs: II. Dynamics in the Griffiths phase of the diluted Ising ferromagnet

International Nuclear Information System (INIS)

Mozeika, A; Coolen, A C C

2009-01-01

We study the Glauber dynamics of Ising spin models with random bonds, on finitely connected random graphs. We generalize a recent dynamical replica theory with which to predict the evolution of the joint spin-field distribution, to include random graphs with arbitrary degree distributions. The theory is applied to Ising ferromagnets on randomly diluted Bethe lattices, where we study the evolution of the magnetization and the internal energy. It predicts a prominent slowing down of the flow in the Griffiths phase, it suggests a further dynamical transition at lower temperatures within the Griffiths phase, and it is verified quantitatively by the results of Monte Carlo simulations

Motifs in triadic random graphs based on Steiner triple systems

Science.gov (United States)

Winkler, Marco; Reichardt, Jörg

2013-08-01

Conventionally, pairwise relationships between nodes are considered to be the fundamental building blocks of complex networks. However, over the last decade, the overabundance of certain subnetwork patterns, i.e., the so-called motifs, has attracted much attention. It has been hypothesized that these motifs, instead of links, serve as the building blocks of network structures. Although the relation between a network's topology and the general properties of the system, such as its function, its robustness against perturbations, or its efficiency in spreading information, is the central theme of network science, there is still a lack of sound generative models needed for testing the functional role of subgraph motifs. Our work aims to overcome this limitation. We employ the framework of exponential random graph models (ERGMs) to define models based on triadic substructures. The fact that only a small portion of triads can actually be set independently poses a challenge for the formulation of such models. To overcome this obstacle, we use Steiner triple systems (STSs). These are partitions of sets of nodes into pair-disjoint triads, which thus can be specified independently. Combining the concepts of ERGMs and STSs, we suggest generative models capable of generating ensembles of networks with nontrivial triadic Z-score profiles. Further, we discover inevitable correlations between the abundance of triad patterns, which occur solely for statistical reasons and need to be taken into account when discussing the functional implications of motif statistics. Moreover, we calculate the degree distributions of our triadic random graphs analytically.

Spectral fluctuations of quantum graphs

International Nuclear Information System (INIS)

Pluhař, Z.; Weidenmüller, H. A.

2014-01-01

We prove the Bohigas-Giannoni-Schmit conjecture in its most general form for completely connected simple graphs with incommensurate bond lengths. We show that for graphs that are classically mixing (i.e., graphs for which the spectrum of the classical Perron-Frobenius operator possesses a finite gap), the generating functions for all (P,Q) correlation functions for both closed and open graphs coincide (in the limit of infinite graph size) with the corresponding expressions of random-matrix theory, both for orthogonal and for unitary symmetry

Graph embedding with rich information through heterogeneous graph

KAUST Repository

Sun, Guolei

2017-11-12

Graph embedding, aiming to learn low-dimensional representations for nodes in graphs, has attracted increasing attention due to its critical application including node classification, link prediction and clustering in social network analysis. Most existing algorithms for graph embedding only rely on the topology information and fail to use the copious information in nodes as well as edges. As a result, their performance for many tasks may not be satisfactory. In this thesis, we proposed a novel and general framework for graph embedding with rich text information (GERI) through constructing a heterogeneous network, in which we integrate node and edge content information with graph topology. Specially, we designed a novel biased random walk to explore the constructed heterogeneous network with the notion of flexible neighborhood. Our sampling strategy can compromise between BFS and DFS local search on heterogeneous graph. To further improve our algorithm, we proposed semi-supervised GERI (SGERI), which learns graph embedding in an discriminative manner through heterogeneous network with label information. The efficacy of our method is demonstrated by extensive comparison experiments with 9 baselines over multi-label and multi-class classification on various datasets including Citeseer, Cora, DBLP and Wiki. It shows that GERI improves the Micro-F1 and Macro-F1 of node classification up to 10%, and SGERI improves GERI by 5% in Wiki.

Generalized connectivity of graphs

CERN Document Server

Li, Xueliang

2016-01-01

Noteworthy results, proof techniques, open problems and conjectures in generalized (edge-) connectivity are discussed in this book. Both theoretical and practical analyses for generalized (edge-) connectivity of graphs are provided. Topics covered in this book include: generalized (edge-) connectivity of graph classes, algorithms, computational complexity, sharp bounds, Nordhaus-Gaddum-type results, maximum generalized local connectivity, extremal problems, random graphs, multigraphs, relations with the Steiner tree packing problem and generalizations of connectivity. This book enables graduate students to understand and master a segment of graph theory and combinatorial optimization. Researchers in graph theory, combinatorics, combinatorial optimization, probability, computer science, discrete algorithms, complexity analysis, network design, and the information transferring models will find this book useful in their studies.

Quantum walks on quotient graphs

International Nuclear Information System (INIS)

Krovi, Hari; Brun, Todd A.

2007-01-01

A discrete-time quantum walk on a graph Γ is the repeated application of a unitary evolution operator to a Hilbert space corresponding to the graph. If this unitary evolution operator has an associated group of symmetries, then for certain initial states the walk will be confined to a subspace of the original Hilbert space. Symmetries of the original graph, given by its automorphism group, can be inherited by the evolution operator. We show that a quantum walk confined to the subspace corresponding to this symmetry group can be seen as a different quantum walk on a smaller quotient graph. We give an explicit construction of the quotient graph for any subgroup H of the automorphism group and illustrate it with examples. The automorphisms of the quotient graph which are inherited from the original graph are the original automorphism group modulo the subgroup H used to construct it. The quotient graph is constructed by removing the symmetries of the subgroup H from the original graph. We then analyze the behavior of hitting times on quotient graphs. Hitting time is the average time it takes a walk to reach a given final vertex from a given initial vertex. It has been shown in earlier work [Phys. Rev. A 74, 042334 (2006)] that the hitting time for certain initial states of a quantum walks can be infinite, in contrast to classical random walks. We give a condition which determines whether the quotient graph has infinite hitting times given that they exist in the original graph. We apply this condition for the examples discussed and determine which quotient graphs have infinite hitting times. All known examples of quantum walks with hitting times which are short compared to classical random walks correspond to systems with quotient graphs much smaller than the original graph; we conjecture that the existence of a small quotient graph with finite hitting times is necessary for a walk to exhibit a quantum speedup

Localization in random bipartite graphs: Numerical and empirical study

Science.gov (United States)

Slanina, František

2017-05-01

We investigate adjacency matrices of bipartite graphs with a power-law degree distribution. Motivation for this study is twofold: first, vibrational states in granular matter and jammed sphere packings; second, graphs encoding social interaction, especially electronic commerce. We establish the position of the mobility edge and show that it strongly depends on the power in the degree distribution and on the ratio of the sizes of the two parts of the bipartite graph. At the jamming threshold, where the two parts have the same size, localization vanishes. We found that the multifractal spectrum is nontrivial in the delocalized phase, but still near the mobility edge. We also study an empirical bipartite graph, namely, the Amazon reviewer-item network. We found that in this specific graph the mobility edge disappears, and we draw a conclusion from this fact regarding earlier empirical studies of the Amazon network.

Coloring geographical threshold graphs

Energy Technology Data Exchange (ETDEWEB)

Bradonjic, Milan [Los Alamos National Laboratory; Percus, Allon [Los Alamos National Laboratory; Muller, Tobias [EINDHOVEN UNIV. OF TECH

2008-01-01

We propose a coloring algorithm for sparse random graphs generated by the geographical threshold graph (GTG) model, a generalization of random geometric graphs (RGG). In a GTG, nodes are distributed in a Euclidean space, and edges are assigned according to a threshold function involving the distance between nodes as well as randomly chosen node weights. The motivation for analyzing this model is that many real networks (e.g., wireless networks, the Internet, etc.) need to be studied by using a 'richer' stochastic model (which in this case includes both a distance between nodes and weights on the nodes). Here, we analyze the GTG coloring algorithm together with the graph's clique number, showing formally that in spite of the differences in structure between GTG and RGG, the asymptotic behavior of the chromatic number is identical: {chi}1n 1n n / 1n n (1 + {omicron}(1)). Finally, we consider the leading corrections to this expression, again using the coloring algorithm and clique number to provide bounds on the chromatic number. We show that the gap between the lower and upper bound is within C 1n n / (1n 1n n){sup 2}, and specify the constant C.

Interacting particle systems on graphs

Science.gov (United States)

Sood, Vishal

In this dissertation, the dynamics of socially or biologically interacting populations are investigated. The individual members of the population are treated as particles that interact via links on a social or biological network represented as a graph. The effect of the structure of the graph on the properties of the interacting particle system is studied using statistical physics techniques. In the first chapter, the central concepts of graph theory and social and biological networks are presented. Next, interacting particle systems that are drawn from physics, mathematics and biology are discussed in the second chapter. In the third chapter, the random walk on a graph is studied. The mean time for a random walk to traverse between two arbitrary sites of a random graph is evaluated. Using an effective medium approximation it is found that the mean first-passage time between pairs of sites, as well as all moments of this first-passage time, are insensitive to the density of links in the graph. The inverse of the mean-first passage time varies non-monotonically with the density of links near the percolation transition of the random graph. Much of the behavior can be understood by simple heuristic arguments. Evolutionary dynamics, by which mutants overspread an otherwise uniform population on heterogeneous graphs, are studied in the fourth chapter. Such a process underlies' epidemic propagation, emergence of fads, social cooperation or invasion of an ecological niche by a new species. The first part of this chapter is devoted to neutral dynamics, in which the mutant genotype does not have a selective advantage over the resident genotype. The time to extinction of one of the two genotypes is derived. In the second part of this chapter, selective advantage or fitness is introduced such that the mutant genotype has a higher birth rate or a lower death rate. This selective advantage leads to a dynamical competition in which selection dominates for large populations

The Little-Hopfield model on a sparse random graph

International Nuclear Information System (INIS)

Castillo, I Perez; Skantzos, N S

2004-01-01

We study the Hopfield model on a random graph in scaling regimes where the average number of connections per neuron is a finite number and the spin dynamics is governed by a synchronous execution of the microscopic update rule (Little-Hopfield model). We solve this model within replica symmetry, and by using bifurcation analysis we prove that the spin-glass/paramagnetic and the retrieval/paramagnetic transition lines of our phase diagram are identical to those of sequential dynamics. The first-order retrieval/spin-glass transition line follows by direct evaluation of our observables using population dynamics. Within the accuracy of numerical precision and for sufficiently small values of the connectivity parameter we find that this line coincides with the corresponding sequential one. Comparison with simulation experiments shows excellent agreement

Random laser emission at dual wavelengths in a donor-acceptor dye mixture solution

Directory of Open Access Journals (Sweden)

Sunita Kedia

Full Text Available The work was aimed to generate random laser emissions simultaneously at two wavelengths in a weakly scattering system containing mixture of binary dyes, rhodamine-B (Rh-B and oxazine-170 (O-170 dispersed with ZnO nano-particles serving as scattering centres. Random lasing performances for individual Rh-B dye were extensively studied for varying small signal gain/scatterer density and we found lasing threshold to significantly depend upon number density of dispersed nano-particles. In spite of inefficient pumping, we demonstrated possibility of random lasing in O-170 dye solution on account of resonance energy transfer from Rh-B dye which served as donor. At optimum concentrations of fluorophores and scatterer in dye mixture solution, incoherent random lasing was effectively attained simultaneously at two wavelengths centered 90 nm apart. Dual-emission intensities, lasing thresholds and rate of amplifications could be controlled and made equivalent for both donor and acceptor in dye mixture solution by appropriate choice of concentrations of dyes and scatterers. Keywords: Random lasing, Energy transfer, Rhodamine-B, Oxazine-170, Zinc oxide

Eigenfunction statistics on quantum graphs

International Nuclear Information System (INIS)

Gnutzmann, S.; Keating, J.P.; Piotet, F.

2010-01-01

We investigate the spatial statistics of the energy eigenfunctions on large quantum graphs. It has previously been conjectured that these should be described by a Gaussian Random Wave Model, by analogy with quantum chaotic systems, for which such a model was proposed by Berry in 1977. The autocorrelation functions we calculate for an individual quantum graph exhibit a universal component, which completely determines a Gaussian Random Wave Model, and a system-dependent deviation. This deviation depends on the graph only through its underlying classical dynamics. Classical criteria for quantum universality to be met asymptotically in the large graph limit (i.e. for the non-universal deviation to vanish) are then extracted. We use an exact field theoretic expression in terms of a variant of a supersymmetric σ model. A saddle-point analysis of this expression leads to the estimates. In particular, intensity correlations are used to discuss the possible equidistribution of the energy eigenfunctions in the large graph limit. When equidistribution is asymptotically realized, our theory predicts a rate of convergence that is a significant refinement of previous estimates. The universal and system-dependent components of intensity correlation functions are recovered by means of an exact trace formula which we analyse in the diagonal approximation, drawing in this way a parallel between the field theory and semiclassics. Our results provide the first instance where an asymptotic Gaussian Random Wave Model has been established microscopically for eigenfunctions in a system with no disorder.

Subsampling for graph power spectrum estimation

KAUST Repository

Chepuri, Sundeep Prabhakar; Leus, Geert

2016-01-01

In this paper we focus on subsampling stationary random signals that reside on the vertices of undirected graphs. Second-order stationary graph signals are obtained by filtering white noise and they admit a well-defined power spectrum. Estimating the graph power spectrum forms a central component of stationary graph signal processing and related inference tasks. We show that by sampling a significantly smaller subset of vertices and using simple least squares, we can reconstruct the power spectrum of the graph signal from the subsampled observations, without any spectral priors. In addition, a near-optimal greedy algorithm is developed to design the subsampling scheme.

Subsampling for graph power spectrum estimation

KAUST Repository

Chepuri, Sundeep Prabhakar

2016-10-06

In this paper we focus on subsampling stationary random signals that reside on the vertices of undirected graphs. Second-order stationary graph signals are obtained by filtering white noise and they admit a well-defined power spectrum. Estimating the graph power spectrum forms a central component of stationary graph signal processing and related inference tasks. We show that by sampling a significantly smaller subset of vertices and using simple least squares, we can reconstruct the power spectrum of the graph signal from the subsampled observations, without any spectral priors. In addition, a near-optimal greedy algorithm is developed to design the subsampling scheme.

Interrelations between random walks on diagrams (graphs) with and without cycles.

Science.gov (United States)

Hill, T L

1988-05-01

Three topics are discussed. A discrete-state, continuous-time random walk with one or more absorption states can be studied by a presumably new method: some mean properties, including the mean time to absorption, can be found from a modified diagram (graph) in which each absorption state is replaced by a one-way cycle back to the starting state. The second problem is a random walk on a diagram (graph) with cycles. The walk terminates on completion of the first cycle. This walk can be replaced by an equivalent walk on a modified diagram with absorption. This absorption diagram can in turn be replaced by another modified diagram with one-way cycles back to the starting state, just as in the first problem. The third problem, important in biophysics, relates to a long-time continuous walk on a diagram with cycles. This diagram can be transformed (in two steps) to a modified, more-detailed, diagram with one-way cycles only. Thus, the one-way cycle fluxes of the original diagram can be found from the state probabilities of the modified diagram. These probabilities can themselves be obtained by simple matrix inversion (the probabilities are determined by linear algebraic steady-state equations). Thus, a simple method is now available to find one-way cycle fluxes exactly (previously Monte Carlo simulation was required to find these fluxes, with attendant fluctuations, for diagrams of any complexity). An incidental benefit of the above procedure is that it provides a simple proof of the one-way cycle flux relation Jn +/- = IIn +/- sigma n/sigma, where n is any cycle of the original diagram.

Structure-reactivity modeling using mixture-based representation of chemical reactions.

Science.gov (United States)

Polishchuk, Pavel; Madzhidov, Timur; Gimadiev, Timur; Bodrov, Andrey; Nugmanov, Ramil; Varnek, Alexandre

2017-09-01

We describe a novel approach of reaction representation as a combination of two mixtures: a mixture of reactants and a mixture of products. In turn, each mixture can be encoded using an earlier reported approach involving simplex descriptors (SiRMS). The feature vector representing these two mixtures results from either concatenated product and reactant descriptors or the difference between descriptors of products and reactants. This reaction representation doesn't need an explicit labeling of a reaction center. The rigorous "product-out" cross-validation (CV) strategy has been suggested. Unlike the naïve "reaction-out" CV approach based on a random selection of items, the proposed one provides with more realistic estimation of prediction accuracy for reactions resulting in novel products. The new methodology has been applied to model rate constants of E2 reactions. It has been demonstrated that the use of the fragment control domain applicability approach significantly increases prediction accuracy of the models. The models obtained with new "mixture" approach performed better than those required either explicit (Condensed Graph of Reaction) or implicit (reaction fingerprints) reaction center labeling.

Polymers and Random graphs: Asymptotic equivalence to branching processes

International Nuclear Information System (INIS)

Spouge, J.L.

1985-01-01

In 1974, Falk and Thomas did a computer simulation of Flory's Equireactive RA/sub f/ Polymer model, rings forbidden and rings allowed. Asymptotically, the Rings Forbidden model tended to Stockmayer's RA/sub f/ distribution (in which the sol distribution ''sticks'' after gelation), while the Rings Allowed model tended to the Flory version of the RA/sub f/ distribution. In 1965, Whittle introduced the Tree and Pseudomultigraph models. We show that these random graphs generalize the Falk and Thomas models by incorporating first-shell substitution effects. Moreover, asymptotically the Tree model displays postgelation ''sticking.'' Hence this phenomenon results from the absence of rings and occurs independently of equireactivity. We also show that the Pseudomultigraph model is asymptotically identical to the Branching Process model introduced by Gordon in 1962. This provides a possible basis for the Branching Process model in standard statistical mechanics

Analytic degree distributions of horizontal visibility graphs mapped from unrelated random series and multifractal binomial measures

Science.gov (United States)

Xie, Wen-Jie; Han, Rui-Qi; Jiang, Zhi-Qiang; Wei, Lijian; Zhou, Wei-Xing

2017-08-01

Complex network is not only a powerful tool for the analysis of complex system, but also a promising way to analyze time series. The algorithm of horizontal visibility graph (HVG) maps time series into graphs, whose degree distributions are numerically and analytically investigated for certain time series. We derive the degree distributions of HVGs through an iterative construction process of HVGs. The degree distributions of the HVG and the directed HVG for random series are derived to be exponential, which confirms the analytical results from other methods. We also obtained the analytical expressions of degree distributions of HVGs and in-degree and out-degree distributions of directed HVGs transformed from multifractal binomial measures, which agree excellently with numerical simulations.

Quantum walk on a chimera graph

Science.gov (United States)

Xu, Shu; Sun, Xiangxiang; Wu, Jizhou; Zhang, Wei-Wei; Arshed, Nigum; Sanders, Barry C.

2018-05-01

We analyse a continuous-time quantum walk on a chimera graph, which is a graph of choice for designing quantum annealers, and we discover beautiful quantum walk features such as localization that starkly distinguishes classical from quantum behaviour. Motivated by technological thrusts, we study continuous-time quantum walk on enhanced variants of the chimera graph and on diminished chimera graph with a random removal of vertices. We explain the quantum walk by constructing a generating set for a suitable subgroup of graph isomorphisms and corresponding symmetry operators that commute with the quantum walk Hamiltonian; the Hamiltonian and these symmetry operators provide a complete set of labels for the spectrum and the stationary states. Our quantum walk characterization of the chimera graph and its variants yields valuable insights into graphs used for designing quantum-annealers.

Generating hierarchial scale-free graphs from fractals

Energy Technology Data Exchange (ETDEWEB)

Komjathy, Julia, E-mail: komyju@math.bme.hu [Department of Stochastics, Institute of Mathematics, Technical University of Budapest, H-1529 P.O. Box 91 (Hungary); Simon, Karoly, E-mail: simonk@math.bme.hu [Department of Stochastics, Institute of Mathematics, Technical University of Budapest, H-1529 P.O. Box 91 (Hungary)

2011-08-15

Highlights: > We generate deterministic scale-free networks using graph-directed self similar IFS. > Our model exhibits similar clustering, power law decay properties to real networks. > The average length of shortest path and the diameter of the graph are determined. > Using this model, we generate random graphs with prescribed power law exponent. - Abstract: Motivated by the hierarchial network model of E. Ravasz, A.-L. Barabasi, and T. Vicsek, we introduce deterministic scale-free networks derived from a graph directed self-similar fractal {Lambda}. With rigorous mathematical results we verify that our model captures some of the most important features of many real networks: the scale-free and the high clustering properties. We also prove that the diameter is the logarithm of the size of the system. We point out a connection between the power law exponent of the degree distribution and some intrinsic geometric measure theoretical properties of the underlying fractal. Using our (deterministic) fractal {Lambda} we generate random graph sequence sharing similar properties.

On the mixing time of geographical threshold graphs

Energy Technology Data Exchange (ETDEWEB)

Bradonjic, Milan [Los Alamos National Laboratory

2009-01-01

In this paper, we study the mixing time of random graphs generated by the geographical threshold graph (GTG) model, a generalization of random geometric graphs (RGG). In a GTG, nodes are distributed in a Euclidean space, and edges are assigned according to a threshold function involving the distance between nodes as well as randomly chosen node weights. The motivation for analyzing this model is that many real networks (e.g., wireless networks, the Internet, etc.) need to be studied by using a 'richer' stochastic model (which in this case includes both a distance between nodes and weights on the nodes). We specifically study the mixing times of random walks on 2-dimensional GTGs near the connectivity threshold. We provide a set of criteria on the distribution of vertex weights that guarantees that the mixing time is {Theta}(n log n).

Towards a theory of geometric graphs

CERN Document Server

Pach, Janos

2004-01-01

The early development of graph theory was heavily motivated and influenced by topological and geometric themes, such as the Konigsberg Bridge Problem, Euler's Polyhedral Formula, or Kuratowski's characterization of planar graphs. In 1936, when Denes Konig published his classical Theory of Finite and Infinite Graphs, the first book ever written on the subject, he stressed this connection by adding the subtitle Combinatorial Topology of Systems of Segments. He wanted to emphasize that the subject of his investigations was very concrete: planar figures consisting of points connected by straight-line segments. However, in the second half of the twentieth century, graph theoretical research took an interesting turn. In the most popular and most rapidly growing areas (the theory of random graphs, Ramsey theory, extremal graph theory, algebraic graph theory, etc.), graphs were considered as abstract binary relations rather than geometric objects. Many of the powerful techniques developed in these fields have been su...

The many faces of graph dynamics

Science.gov (United States)

Pignolet, Yvonne Anne; Roy, Matthieu; Schmid, Stefan; Tredan, Gilles

2017-06-01

The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is known today about the network dynamics: indeed, complex networks in reality are not static, but rather dynamically evolve over time. Our paper is motivated by the empirical observation that network evolution patterns seem far from random, but exhibit structure. Moreover, the specific patterns appear to depend on the network type, contradicting the existence of a ‘one fits it all’ model. However, we still lack observables to quantify these intuitions, as well as metrics to compare graph evolutions. Such observables and metrics are needed for extrapolating or predicting evolutions, as well as for interpolating graph evolutions. To explore the many faces of graph dynamics and to quantify temporal changes, this paper suggests to build upon the concept of centrality, a measure of node importance in a network. In particular, we introduce the notion of centrality distance, a natural similarity measure for two graphs which depends on a given centrality, characterizing the graph type. Intuitively, centrality distances reflect the extent to which (non-anonymous) node roles are different or, in case of dynamic graphs, have changed over time, between two graphs. We evaluate the centrality distance approach for five evolutionary models and seven real-world social and physical networks. Our results empirically show the usefulness of centrality distances for characterizing graph dynamics compared to a null-model of random evolution, and highlight the differences between the considered scenarios. Interestingly, our approach allows us to compare the dynamics of very different networks, in terms of scale and evolution speed.

Graphs of groups on surfaces interactions and models

CERN Document Server

White, AT

2001-01-01

The book, suitable as both an introductory reference and as a text book in the rapidly growing field of topological graph theory, models both maps (as in map-coloring problems) and groups by means of graph imbeddings on sufaces. Automorphism groups of both graphs and maps are studied. In addition connections are made to other areas of mathematics, such as hypergraphs, block designs, finite geometries, and finite fields. There are chapters on the emerging subfields of enumerative topological graph theory and random topological graph theory, as well as a chapter on the composition of English

Graph theoretical model of a sensorimotor connectome in zebrafish.

Science.gov (United States)

Stobb, Michael; Peterson, Joshua M; Mazzag, Borbala; Gahtan, Ethan

2012-01-01

Mapping the detailed connectivity patterns (connectomes) of neural circuits is a central goal of neuroscience. The best quantitative approach to analyzing connectome data is still unclear but graph theory has been used with success. We present a graph theoretical model of the posterior lateral line sensorimotor pathway in zebrafish. The model includes 2,616 neurons and 167,114 synaptic connections. Model neurons represent known cell types in zebrafish larvae, and connections were set stochastically following rules based on biological literature. Thus, our model is a uniquely detailed computational representation of a vertebrate connectome. The connectome has low overall connection density, with 2.45% of all possible connections, a value within the physiological range. We used graph theoretical tools to compare the zebrafish connectome graph to small-world, random and structured random graphs of the same size. For each type of graph, 100 randomly generated instantiations were considered. Degree distribution (the number of connections per neuron) varied more in the zebrafish graph than in same size graphs with less biological detail. There was high local clustering and a short average path length between nodes, implying a small-world structure similar to other neural connectomes and complex networks. The graph was found not to be scale-free, in agreement with some other neural connectomes. An experimental lesion was performed that targeted three model brain neurons, including the Mauthner neuron, known to control fast escape turns. The lesion decreased the number of short paths between sensory and motor neurons analogous to the behavioral effects of the same lesion in zebrafish. This model is expandable and can be used to organize and interpret a growing database of information on the zebrafish connectome.

Functionals of Brownian motion, localization and metric graphs

International Nuclear Information System (INIS)

Comtet, Alain; Desbois, Jean; Texier, Christophe

2005-01-01

We review several results related to the problem of a quantum particle in a random environment. In an introductory part, we recall how several functionals of Brownian motion arise in the study of electronic transport in weakly disordered metals (weak localization). Two aspects of the physics of the one-dimensional strong localization are reviewed: some properties of the scattering by a random potential (time delay distribution) and a study of the spectrum of a random potential on a bounded domain (the extreme value statistics of the eigenvalues). Then we mention several results concerning the diffusion on graphs, and more generally the spectral properties of the Schroedinger operator on graphs. The interest of spectral determinants as generating functions characterizing the diffusion on graphs is illustrated. Finally, we consider a two-dimensional model of a charged particle coupled to the random magnetic field due to magnetic vortices. We recall the connection between spectral properties of this model and winding functionals of planar Brownian motion. (topical review)

A tree-decomposed transfer matrix for computing exact Potts model partition functions for arbitrary graphs, with applications to planar graph colourings

International Nuclear Information System (INIS)

Bedini, Andrea; Jacobsen, Jesper Lykke

2010-01-01

Combining tree decomposition and transfer matrix techniques provides a very general algorithm for computing exact partition functions of statistical models defined on arbitrary graphs. The algorithm is particularly efficient in the case of planar graphs. We illustrate it by computing the Potts model partition functions and chromatic polynomials (the number of proper vertex colourings using Q colours) for large samples of random planar graphs with up to N = 100 vertices. In the latter case, our algorithm yields a sub-exponential average running time of ∼ exp(1.516√N), a substantial improvement over the exponential running time ∼exp (0.245N) provided by the hitherto best-known algorithm. We study the statistics of chromatic roots of random planar graphs in some detail, comparing the findings with results for finite pieces of a regular lattice.

Giant Components in Biased Graph Processes

OpenAIRE

Amir, Gideon; Gurel-Gurevich, Ori; Lubetzky, Eyal; Singer, Amit

2005-01-01

A random graph process, $\\Gorg[1](n)$, is a sequence of graphs on $n$ vertices which begins with the edgeless graph, and where at each step a single edge is added according to a uniform distribution on the missing edges. It is well known that in such a process a giant component (of linear size) typically emerges after $(1+o(1))\\frac{n}{2}$ edges (a phenomenon known as ``the double jump''), i.e., at time $t=1$ when using a timescale of $n/2$ edges in each step. We consider a generalization of ...

Graph theoretical model of a sensorimotor connectome in zebrafish.

Directory of Open Access Journals (Sweden)

Michael Stobb

Full Text Available Mapping the detailed connectivity patterns (connectomes of neural circuits is a central goal of neuroscience. The best quantitative approach to analyzing connectome data is still unclear but graph theory has been used with success. We present a graph theoretical model of the posterior lateral line sensorimotor pathway in zebrafish. The model includes 2,616 neurons and 167,114 synaptic connections. Model neurons represent known cell types in zebrafish larvae, and connections were set stochastically following rules based on biological literature. Thus, our model is a uniquely detailed computational representation of a vertebrate connectome. The connectome has low overall connection density, with 2.45% of all possible connections, a value within the physiological range. We used graph theoretical tools to compare the zebrafish connectome graph to small-world, random and structured random graphs of the same size. For each type of graph, 100 randomly generated instantiations were considered. Degree distribution (the number of connections per neuron varied more in the zebrafish graph than in same size graphs with less biological detail. There was high local clustering and a short average path length between nodes, implying a small-world structure similar to other neural connectomes and complex networks. The graph was found not to be scale-free, in agreement with some other neural connectomes. An experimental lesion was performed that targeted three model brain neurons, including the Mauthner neuron, known to control fast escape turns. The lesion decreased the number of short paths between sensory and motor neurons analogous to the behavioral effects of the same lesion in zebrafish. This model is expandable and can be used to organize and interpret a growing database of information on the zebrafish connectome.

graphkernels: R and Python packages for graph comparison.

Science.gov (United States)

Sugiyama, Mahito; Ghisu, M Elisabetta; Llinares-López, Felipe; Borgwardt, Karsten

2018-02-01

Measuring the similarity of graphs is a fundamental step in the analysis of graph-structured data, which is omnipresent in computational biology. Graph kernels have been proposed as a powerful and efficient approach to this problem of graph comparison. Here we provide graphkernels, the first R and Python graph kernel libraries including baseline kernels such as label histogram based kernels, classic graph kernels such as random walk based kernels, and the state-of-the-art Weisfeiler-Lehman graph kernel. The core of all graph kernels is implemented in C ++ for efficiency. Using the kernel matrices computed by the package, we can easily perform tasks such as classification, regression and clustering on graph-structured samples. The R and Python packages including source code are available at https://CRAN.R-project.org/package=graphkernels and https://pypi.python.org/pypi/graphkernels. mahito@nii.ac.jp or elisabetta.ghisu@bsse.ethz.ch. Supplementary data are available online at Bioinformatics. © The Author(s) 2017. Published by Oxford University Press.

Mixture-mixture design for the fingerprint optimization of chromatographic mobile phases and extraction solutions for Camellia sinensis.

Science.gov (United States)

Borges, Cleber N; Bruns, Roy E; Almeida, Aline A; Scarminio, Ieda S

2007-07-09

A composite simplex centroid-simplex centroid mixture design is proposed for simultaneously optimizing two mixture systems. The complementary model is formed by multiplying special cubic models for the two systems. The design was applied to the simultaneous optimization of both mobile phase chromatographic mixtures and extraction mixtures for the Camellia sinensis Chinese tea plant. The extraction mixtures investigated contained varying proportions of ethyl acetate, ethanol and dichloromethane while the mobile phase was made up of varying proportions of methanol, acetonitrile and a methanol-acetonitrile-water (MAW) 15%:15%:70% mixture. The experiments were block randomized corresponding to a split-plot error structure to minimize laboratory work and reduce environmental impact. Coefficients of an initial saturated model were obtained using Scheffe-type equations. A cumulative probability graph was used to determine an approximate reduced model. The split-plot error structure was then introduced into the reduced model by applying generalized least square equations with variance components calculated using the restricted maximum likelihood approach. A model was developed to calculate the number of peaks observed with the chromatographic detector at 210 nm. A 20-term model contained essentially all the statistical information of the initial model and had a root mean square calibration error of 1.38. The model was used to predict the number of peaks eluted in chromatograms obtained from extraction solutions that correspond to axial points of the simplex centroid design. The significant model coefficients are interpreted in terms of interacting linear, quadratic and cubic effects of the mobile phase and extraction solution components.

A multi-directional rapidly exploring random graph (mRRG) for protein folding

KAUST Repository

Nath, Shuvra Kanti; Thomas, Shawna; Ekenna, Chinwe; Amato, Nancy M.

2012-01-01

Modeling large-scale protein motions, such as those involved in folding and binding interactions, is crucial to better understanding not only how proteins move and interact with other molecules but also how proteins misfold, thus causing many devastating diseases. Robotic motion planning algorithms, such as Rapidly Exploring Random Trees (RRTs), have been successful in simulating protein folding pathways. Here, we propose a new multi-directional Rapidly Exploring Random Graph (mRRG) specifically tailored for proteins. Unlike traditional RRGs which only expand a parent conformation in a single direction, our strategy expands the parent conformation in multiple directions to generate new samples. Resulting samples are connected to the parent conformation and its nearest neighbors. By leveraging multiple directions, mRRG can model the protein motion landscape with reduced computational time compared to several other robotics-based methods for small to moderate-sized proteins. Our results on several proteins agree with experimental hydrogen out-exchange, pulse-labeling, and F-value analysis. We also show that mRRG covers the conformation space better as compared to the other computation methods. Copyright © 2012 ACM.

Improving Estimation of Betweenness Centrality for Scale-Free Graphs

Energy Technology Data Exchange (ETDEWEB)

Bromberger, Seth A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Klymko, Christine F. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Henderson, Keith A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Pearce, Roger [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Sanders, Geoff [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

2017-11-07

Betweenness centrality is a graph statistic used to nd vertices that are participants in a large number of shortest paths in a graph. This centrality measure is commonly used in path and network interdiction problems and its complete form requires the calculation of all-pairs shortest paths for each vertex. This leads to a time complexity of O(jV jjEj), which is impractical for large graphs. Estimation of betweenness centrality has focused on performing shortest-path calculations on a subset of randomly- selected vertices. This reduces the complexity of the centrality estimation to O(jSjjEj); jSj < jV j, which can be scaled appropriately based on the computing resources available. An estimation strategy that uses random selection of vertices for seed selection is fast and simple to implement, but may not provide optimal estimation of betweenness centrality when the number of samples is constrained. Our experimentation has identi ed a number of alternate seed-selection strategies that provide lower error than random selection in common scale-free graphs. These strategies are discussed and experimental results are presented.

An Xdata Architecture for Federated Graph Models and Multi-tier Asymmetric Computing

Science.gov (United States)

2014-01-01

Wikipedia, a scale-free random graph (kron), Akamai trace route data, Bitcoin transaction data, and a Twitter follower network. We present results for...3x (SSSP on a random graph) and nearly 300x (Akamai and Bitcoin ) over the CPU performance of a well-known and widely deployed CPU-based graph...provided better throughput for smaller frontiers such as roadmaps or the Bitcoin data set. In our work, we have focused on two-phase kernels, but it

An internet graph model based on trade-off optimization

Science.gov (United States)

Alvarez-Hamelin, J. I.; Schabanel, N.

2004-03-01

This paper presents a new model for the Internet graph (AS graph) based on the concept of heuristic trade-off optimization, introduced by Fabrikant, Koutsoupias and Papadimitriou in[CITE] to grow a random tree with a heavily tailed degree distribution. We propose here a generalization of this approach to generate a general graph, as a candidate for modeling the Internet. We present the results of our simulations and an analysis of the standard parameters measured in our model, compared with measurements from the physical Internet graph.

Distributed Large Independent Sets in One Round On Bounded-independence Graphs

OpenAIRE

Halldorsson , Magnus M.; Konrad , Christian

2015-01-01

International audience; We present a randomized one-round, single-bit messages, distributed algorithm for the maximum independent set problem in polynomially bounded-independence graphs with poly-logarithmic approximation factor. Bounded-independence graphs capture various models of wireless networks such as the unit disc graphs model and the quasi unit disc graphs model. For instance, on unit disc graphs, our achieved approximation ratio is O((log(n)/log(log(n)))^2).A starting point of our w...

Summing Feynman graphs by Monte Carlo: Planar φ3-theory and dynamically triangulated random surfaces

International Nuclear Information System (INIS)

Boulatov, D.V.

1988-01-01

New combinatorial identities are suggested relating the ratio of (n-1)th and nth orders of (planar) perturbation expansion for any quantity to some average over the ensemble of all planar graphs of the nth order. These identities are used for Monte Carlo calculation of critical exponents γ str (string susceptibility) in planar φ 3 -theory and in the dynamically triangulated random surface (DTRS) model near the convergence circle for various dimensions. In the solvable case D=1 the exact critical properties of the theory are reproduced numerically. (orig.)

An Efficient Monte Carlo Approach to Compute PageRank for Large Graphs on a Single PC

Directory of Open Access Journals (Sweden)

Sonobe Tomohiro

2016-03-01

Full Text Available This paper describes a novel Monte Carlo based random walk to compute PageRanks of nodes in a large graph on a single PC. The target graphs of this paper are ones whose size is larger than the physical memory. In such an environment, memory management is a difficult task for simulating the random walk among the nodes. We propose a novel method that partitions the graph into subgraphs in order to make them fit into the physical memory, and conducts the random walk for each subgraph. By evaluating the walks lazily, we can conduct the walks only in a subgraph and approximate the random walk by rotating the subgraphs. In computational experiments, the proposed method exhibits good performance for existing large graphs with several passes of the graph data.

Efficient Sampling of the Structure of Crypto Generators' State Transition Graphs

Science.gov (United States)

Keller, Jörg

Cryptographic generators, e.g. stream cipher generators like the A5/1 used in GSM networks or pseudo-random number generators, are widely used in cryptographic network protocols. Basically, they are finite state machines with deterministic transition functions. Their state transition graphs typically cannot be analyzed analytically, nor can they be explored completely because of their size which typically is at least n = 264. Yet, their structure, i.e. number and sizes of weakly connected components, is of interest because a structure deviating significantly from expected values for random graphs may form a distinguishing attack that indicates a weakness or backdoor. By sampling, one randomly chooses k nodes, derives their distribution onto connected components by graph exploration, and extrapolates these results to the complete graph. In known algorithms, the computational cost to determine the component for one randomly chosen node is up to O(√n), which severely restricts the sample size k. We present an algorithm where the computational cost to find the connected component for one randomly chosen node is O(1), so that a much larger sample size k can be analyzed in a given time. We report on the performance of a prototype implementation, and about preliminary analysis for several generators.

Low-algorithmic-complexity entropy-deceiving graphs

KAUST Repository

Zenil, Hector

2017-07-08

In estimating the complexity of objects, in particular, of graphs, it is common practice to rely on graphand information-theoretic measures. Here, using integer sequences with properties such as Borel normality, we explain how these measures are not independent of the way in which an object, such as a graph, can be described or observed. From observations that can reconstruct the same graph and are therefore essentially translations of the same description, we see that when applying a computable measure such as the Shannon entropy, not only is it necessary to preselect a feature of interest where there is one, and to make an arbitrary selection where there is not, but also more general properties, such as the causal likelihood of a graph as a measure (opposed to randomness), can be largely misrepresented by computable measures such as the entropy and entropy rate. We introduce recursive and nonrecursive (uncomputable) graphs and graph constructions based on these integer sequences, whose different lossless descriptions have disparate entropy values, thereby enabling the study and exploration of a measure\\'s range of applications and demonstrating the weaknesses of computable measures of complexity.

Low-algorithmic-complexity entropy-deceiving graphs

KAUST Repository

Zenil, Hector; Kiani, Narsis A.; Tegner, Jesper

2017-01-01

In estimating the complexity of objects, in particular, of graphs, it is common practice to rely on graphand information-theoretic measures. Here, using integer sequences with properties such as Borel normality, we explain how these measures are not independent of the way in which an object, such as a graph, can be described or observed. From observations that can reconstruct the same graph and are therefore essentially translations of the same description, we see that when applying a computable measure such as the Shannon entropy, not only is it necessary to preselect a feature of interest where there is one, and to make an arbitrary selection where there is not, but also more general properties, such as the causal likelihood of a graph as a measure (opposed to randomness), can be largely misrepresented by computable measures such as the entropy and entropy rate. We introduce recursive and nonrecursive (uncomputable) graphs and graph constructions based on these integer sequences, whose different lossless descriptions have disparate entropy values, thereby enabling the study and exploration of a measure's range of applications and demonstrating the weaknesses of computable measures of complexity.

Dynamic airspace configuration method based on a weighted graph model

Directory of Open Access Journals (Sweden)

Chen Yangzhou

2014-08-01

Full Text Available This paper proposes a new method for dynamic airspace configuration based on a weighted graph model. The method begins with the construction of an undirected graph for the given airspace, where the vertices represent those key points such as airports, waypoints, and the edges represent those air routes. Those vertices are used as the sites of Voronoi diagram, which divides the airspace into units called as cells. Then, aircraft counts of both each cell and of each air-route are computed. Thus, by assigning both the vertices and the edges with those aircraft counts, a weighted graph model comes into being. Accordingly the airspace configuration problem is described as a weighted graph partitioning problem. Then, the problem is solved by a graph partitioning algorithm, which is a mixture of general weighted graph cuts algorithm, an optimal dynamic load balancing algorithm and a heuristic algorithm. After the cuts algorithm partitions the model into sub-graphs, the load balancing algorithm together with the heuristic algorithm transfers aircraft counts to balance workload among sub-graphs. Lastly, airspace configuration is completed by determining the sector boundaries. The simulation result shows that the designed sectors satisfy not only workload balancing condition, but also the constraints such as convexity, connectivity, as well as minimum distance constraint.

Pristine transfinite graphs and permissive electrical networks

CERN Document Server

Zemanian, Armen H

2001-01-01

A transfinite graph or electrical network of the first rank is obtained conceptually by connecting conventionally infinite graphs and networks together at their infinite extremities. This process can be repeated to obtain a hierarchy of transfiniteness whose ranks increase through the countable ordinals. This idea, which is of recent origin, has enriched the theories of graphs and networks with radically new constructs and research problems. The book provides a more accessible introduction to the subject that, though sacrificing some generality, captures the essential ideas of transfiniteness for graphs and networks. Thus, for example, some results concerning discrete potentials and random walks on transfinite networks can now be presented more concisely. Conversely, the simplifications enable the development of many new results that were previously unavailable. Topics and features: *A simplified exposition provides an introduction to transfiniteness for graphs and networks.*Various results for conventional g...

Sampling Large Graphs for Anticipatory Analytics

Science.gov (United States)

2015-05-15

low. C. Random Area Sampling Random area sampling [8] is a “ snowball ” sampling method in which a set of random seed vertices are selected and areas... Sampling Large Graphs for Anticipatory Analytics Lauren Edwards, Luke Johnson, Maja Milosavljevic, Vijay Gadepally, Benjamin A. Miller Lincoln...systems, greater human-in-the-loop involvement, or through complex algorithms. We are investigating the use of sampling to mitigate these challenges

Generalized random sequential adsorption of polydisperse mixtures on a one-dimensional lattice

International Nuclear Information System (INIS)

Lončarević, I; Budinski-Petković, Lj; Vrhovac, S B; Belić, A

2010-01-01

Generalized random sequential adsorption (RSA) of polydisperse mixtures of k-mers on a one-dimensional lattice is studied numerically by means of Monte Carlo simulations. The kinetics of the deposition process of mixtures is studied for the irreversible case, for adsorption–desorption processes and for the case where adsorption, desorption and diffusion are present simultaneously. We concentrate here on the influence of the number of mixture components and the length of the k-mers making up the mixture on the temporal behavior of the coverage fraction θ(t). The approach of the coverage θ(t) to the jamming limit θ jam in the case of irreversible RSA is found to be exponential, θ jam -θ(t)∝ exp(-t/σ), not only for a whole mixture, but also for the individual components. For the reversible deposition of polydisperse mixtures, we find that after the initial 'jamming', a stretched exponential growth of the coverage θ(t) towards the equilibrium state value θ eq occurs, i.e., θ eq -θ(t)∝ exp[-(t/τ) β ]. The characteristic timescale τ is found to decrease with the desorption probability P des . When adsorption, desorption and diffusion occur simultaneously, the coverage of a mixture always reaches an equilibrium value θ eq , but there is a significant difference in temporal evolution between the coverage with diffusion and that without

The heat kernel as the pagerank of a graph

Science.gov (United States)

Chung, Fan

2007-01-01

The concept of pagerank was first started as a way for determining the ranking of Web pages by Web search engines. Based on relations in interconnected networks, pagerank has become a major tool for addressing fundamental problems arising in general graphs, especially for large information networks with hundreds of thousands of nodes. A notable notion of pagerank, introduced by Brin and Page and denoted by PageRank, is based on random walks as a geometric sum. In this paper, we consider a notion of pagerank that is based on the (discrete) heat kernel and can be expressed as an exponential sum of random walks. The heat kernel satisfies the heat equation and can be used to analyze many useful properties of random walks in a graph. A local Cheeger inequality is established, which implies that, by focusing on cuts determined by linear orderings of vertices using the heat kernel pageranks, the resulting partition is within a quadratic factor of the optimum. This is true, even if we restrict the volume of the small part separated by the cut to be close to some specified target value. This leads to a graph partitioning algorithm for which the running time is proportional to the size of the targeted volume (instead of the size of the whole graph).

A characterization of horizontal visibility graphs and combinatorics on words

Science.gov (United States)

Gutin, Gregory; Mansour, Toufik; Severini, Simone

2011-06-01

A Horizontal Visibility Graph (HVG) is defined in association with an ordered set of non-negative reals. HVGs realize a methodology in the analysis of time series, their degree distribution being a good discriminator between randomness and chaos Luque et al. [B. Luque, L. Lacasa, F. Ballesteros, J. Luque, Horizontal visibility graphs: exact results for random time series, Phys. Rev. E 80 (2009), 046103]. We prove that a graph is an HVG if and only if it is outerplanar and has a Hamilton path. Therefore, an HVG is a noncrossing graph, as defined in algebraic combinatorics Flajolet and Noy [P. Flajolet, M. Noy, Analytic combinatorics of noncrossing configurations, Discrete Math., 204 (1999) 203-229]. Our characterization of HVGs implies a linear time recognition algorithm. Treating ordered sets as words, we characterize subfamilies of HVGs highlighting various connections with combinatorial statistics and introducing the notion of a visible pair. With this technique, we determine asymptotically the average number of edges of HVGs.

White random lasing in mixture of ZnSe, CdS and CdSSe micropowders

Science.gov (United States)

Alyamani, A. Y.; Leanenia, M. S.; Alanazi, L. M.; Aljohani, M. M.; Aljariwi, A. A.; Rzheutski, M. V.; Lutsenko, E. V.; Yablonskii, G. P.

2016-03-01

Room temperature random lasing with white light emission in a mixture of AIIBVI semiconductor powders was achieved for the first time. The scattering gain media was formed by the mixture of closely packed active micron sized crystallites of ZnSe, CdS, CdSSe semiconductors. The micropowders were produced by grinding bulk crystals of each compound. Optical excitation was performed by 10-nanosecond pulses of tuned Ti:Al2O3-laser at 390 nm. The lasing in the mixture of semiconductor powders was achieved simultaneously at four wavelengths in blue, green, yellow and red spectral regions after exceeding the threshold excitation power density. A drastic integral intensity increase, spectrum narrowing and appearance of mode structure accompanied the laser action. ZnSe crystallites produce the laser light at about 460 nm while CdS particles - at about 520 nm. Two types of CdSSe semiconductor micropowders with different sulfur content lase at 580 nm and 660 nm. The threshold excitation power densities for all laser lines in the emission spectrum are approximately the same of about 0.9 MW/cm2. The sum of the emission spectrum of the mixture of the micropowders forms white light with high brightness. Lasing is due to an appearance of random feedback for amplified radiation in the active medium of closely packed light scattering crystallites. The presented results may find their applications for visualization systems, lighting technology, data transmission, medicine as biosensors and in identification systems. The key feature of random lasers is low cost of its production and possibility to be deposited on any type of surface.

Skin Segmentation Based on Graph Cuts

Institute of Scientific and Technical Information of China (English)

HU Zhilan; WANG Guijin; LIN Xinggang; YAN Hong

2009-01-01

Skin segmentation is widely used in many computer vision tasks to improve automated visualiza-tion. This paper presents a graph cuts algorithm to segment arbitrary skin regions from images. The detected face is used to determine the foreground skin seeds and the background non-skin seeds with the color probability distributions for the foreground represented by a single Gaussian model and for the background by a Gaussian mixture model. The probability distribution of the image is used for noise suppression to alle-viate the influence of the background regions having skin-like colors. Finally, the skin is segmented by graph cuts, with the regional parameter y optimally selected to adapt to different images. Tests of the algorithm on many real wodd photographs show that the scheme accurately segments skin regions and is robust against illumination variations, individual skin variations, and cluttered backgrounds.

Laplacian Estrada and normalized Laplacian Estrada indices of evolving graphs.

Science.gov (United States)

Shang, Yilun

2015-01-01

Large-scale time-evolving networks have been generated by many natural and technological applications, posing challenges for computation and modeling. Thus, it is of theoretical and practical significance to probe mathematical tools tailored for evolving networks. In this paper, on top of the dynamic Estrada index, we study the dynamic Laplacian Estrada index and the dynamic normalized Laplacian Estrada index of evolving graphs. Using linear algebra techniques, we established general upper and lower bounds for these graph-spectrum-based invariants through a couple of intuitive graph-theoretic measures, including the number of vertices or edges. Synthetic random evolving small-world networks are employed to show the relevance of the proposed dynamic Estrada indices. It is found that neither the static snapshot graphs nor the aggregated graph can approximate the evolving graph itself, indicating the fundamental difference between the static and dynamic Estrada indices.

A graph rewriting programming language for graph drawing

OpenAIRE

Rodgers, Peter

1998-01-01

This paper describes Grrr, a prototype visual graph drawing tool. Previously there were no visual languages for programming graph drawing algorithms despite the inherently visual nature of the process. The languages which gave a diagrammatic view of graphs were not computationally complete and so could not be used to implement complex graph drawing algorithms. Hence current graph drawing tools are all text based. Recent developments in graph rewriting systems have produced computationally com...

Ising model of a randomly triangulated random surface as a definition of fermionic string theory

International Nuclear Information System (INIS)

Bershadsky, M.A.; Migdal, A.A.

1986-01-01

Fermionic degrees of freedom are added to randomly triangulated planar random surfaces. It is shown that the Ising model on a fixed graph is equivalent to a certain Majorana fermion theory on the dual graph. (orig.)

Almost all k-cop-win graphs contain a dominating set of cardinality k

OpenAIRE

Pralat, Pawel

2013-01-01

We consider $k$-cop-win graphs in the binomial random graph $G(n,1/2).$ It is known that almost all cop-win graphs contain a universal vertex. We generalize this result and prove that for every $k \\in N$, almost all $k$-cop-win graphs contain a dominating set of cardinality $k$. From this it follows that the asymptotic number of labelled $k$-cop-win graphs of order $n$ is equal to $(1+o(1)) (1-2^{-k})^{-k} {n \\choose k} 2^{n^2/2 - (1/2-\\log_2(1-2^{-k})) n}$.

Encrypted data stream identification using randomness sparse representation and fuzzy Gaussian mixture model

Science.gov (United States)

Zhang, Hong; Hou, Rui; Yi, Lei; Meng, Juan; Pan, Zhisong; Zhou, Yuhuan

2016-07-01

The accurate identification of encrypted data stream helps to regulate illegal data, detect network attacks and protect users' information. In this paper, a novel encrypted data stream identification algorithm is introduced. The proposed method is based on randomness characteristics of encrypted data stream. We use a l1-norm regularized logistic regression to improve sparse representation of randomness features and Fuzzy Gaussian Mixture Model (FGMM) to improve identification accuracy. Experimental results demonstrate that the method can be adopted as an effective technique for encrypted data stream identification.

Efficient Graph Computation for Node2Vec

OpenAIRE

Zhou, Dongyan; Niu, Songjie; Chen, Shimin

2018-01-01

Node2Vec is a state-of-the-art general-purpose feature learning method for network analysis. However, current solutions cannot run Node2Vec on large-scale graphs with billions of vertices and edges, which are common in real-world applications. The existing distributed Node2Vec on Spark incurs significant space and time overhead. It runs out of memory even for mid-sized graphs with millions of vertices. Moreover, it considers at most 30 edges for every vertex in generating random walks, causin...

Laplacian Estrada and normalized Laplacian Estrada indices of evolving graphs.

Directory of Open Access Journals (Sweden)

Yilun Shang

Full Text Available Large-scale time-evolving networks have been generated by many natural and technological applications, posing challenges for computation and modeling. Thus, it is of theoretical and practical significance to probe mathematical tools tailored for evolving networks. In this paper, on top of the dynamic Estrada index, we study the dynamic Laplacian Estrada index and the dynamic normalized Laplacian Estrada index of evolving graphs. Using linear algebra techniques, we established general upper and lower bounds for these graph-spectrum-based invariants through a couple of intuitive graph-theoretic measures, including the number of vertices or edges. Synthetic random evolving small-world networks are employed to show the relevance of the proposed dynamic Estrada indices. It is found that neither the static snapshot graphs nor the aggregated graph can approximate the evolving graph itself, indicating the fundamental difference between the static and dynamic Estrada indices.

A class of stochastic games with infinitely many interacting agents related to Glauber dynamics on random graphs

International Nuclear Information System (INIS)

De Santis, Emilio; Marinelli, Carlo

2007-01-01

We introduce and study a class of infinite-horizon non-zero-sum non-cooperative stochastic games with infinitely many interacting agents using ideas of statistical mechanics. First we show, in the general case of asymmetric interactions, the existence of a strategy that allows any player to eliminate losses after a finite random time. In the special case of symmetric interactions, we also prove that, as time goes to infinity, the game converges to a Nash equilibrium. Moreover, assuming that all agents adopt the same strategy, using arguments related to those leading to perfect simulation algorithms, spatial mixing and ergodicity are proved. In turn, ergodicity allows us to prove 'fixation', i.e. players will adopt a constant strategy after a finite time. The resulting dynamics is related to zero-temperature Glauber dynamics on random graphs of possibly infinite volume

Graph Aggregation

NARCIS (Netherlands)

Endriss, U.; Grandi, U.

Graph aggregation is the process of computing a single output graph that constitutes a good compromise between several input graphs, each provided by a different source. One needs to perform graph aggregation in a wide variety of situations, e.g., when applying a voting rule (graphs as preference

Partition function expansion on region graphs and message-passing equations

International Nuclear Information System (INIS)

Zhou, Haijun; Wang, Chuang; Xiao, Jing-Qing; Bi, Zedong

2011-01-01

Disordered and frustrated graphical systems are ubiquitous in physics, biology, and information science. For models on complete graphs or random graphs, deep understanding has been achieved through the mean-field replica and cavity methods. But finite-dimensional 'real' systems remain very challenging because of the abundance of short loops and strong local correlations. A statistical mechanics theory is constructed in this paper for finite-dimensional models based on the mathematical framework of the partition function expansion and the concept of region graphs. Rigorous expressions for the free energy and grand free energy are derived. Message-passing equations on the region graph, such as belief propagation and survey propagation, are also derived rigorously. (letter)

Nonlinear complexity of random visibility graph and Lempel-Ziv on multitype range-intensity interacting financial dynamics

Science.gov (United States)

Zhang, Yali; Wang, Jun

2017-09-01

In an attempt to investigate the nonlinear complex evolution of financial dynamics, a new financial price model - the multitype range-intensity contact (MRIC) financial model, is developed based on the multitype range-intensity interacting contact system, in which the interaction and transmission of different types of investment attitudes in a stock market are simulated by viruses spreading. Two new random visibility graph (VG) based analyses and Lempel-Ziv complexity (LZC) are applied to study the complex behaviors of return time series and the corresponding random sorted series. The VG method is the complex network theory, and the LZC is a non-parametric measure of complexity reflecting the rate of new pattern generation of a series. In this work, the real stock market indices are considered to be comparatively studied with the simulation data of the proposed model. Further, the numerical empirical study shows the similar complexity behaviors between the model and the real markets, the research confirms that the financial model is reasonable to some extent.

Proxy Graph: Visual Quality Metrics of Big Graph Sampling.

Science.gov (United States)

Nguyen, Quan Hoang; Hong, Seok-Hee; Eades, Peter; Meidiana, Amyra

2017-06-01

Data sampling has been extensively studied for large scale graph mining. Many analyses and tasks become more efficient when performed on graph samples of much smaller size. The use of proxy objects is common in software engineering for analysis and interaction with heavy objects or systems. In this paper, we coin the term 'proxy graph' and empirically investigate how well a proxy graph visualization can represent a big graph. Our investigation focuses on proxy graphs obtained by sampling; this is one of the most common proxy approaches. Despite the plethora of data sampling studies, this is the first evaluation of sampling in the context of graph visualization. For an objective evaluation, we propose a new family of quality metrics for visual quality of proxy graphs. Our experiments cover popular sampling techniques. Our experimental results lead to guidelines for using sampling-based proxy graphs in visualization.

Betweenness-based algorithm for a partition scale-free graph

International Nuclear Information System (INIS)

Zhang Bai-Da; Wu Jun-Jie; Zhou Jing; Tang Yu-Hua

2011-01-01

Many real-world networks are found to be scale-free. However, graph partition technology, as a technology capable of parallel computing, performs poorly when scale-free graphs are provided. The reason for this is that traditional partitioning algorithms are designed for random networks and regular networks, rather than for scale-free networks. Multilevel graph-partitioning algorithms are currently considered to be the state of the art and are used extensively. In this paper, we analyse the reasons why traditional multilevel graph-partitioning algorithms perform poorly and present a new multilevel graph-partitioning paradigm, top down partitioning, which derives its name from the comparison with the traditional bottom—up partitioning. A new multilevel partitioning algorithm, named betweenness-based partitioning algorithm, is also presented as an implementation of top—down partitioning paradigm. An experimental evaluation of seven different real-world scale-free networks shows that the betweenness-based partitioning algorithm significantly outperforms the existing state-of-the-art approaches. (interdisciplinary physics and related areas of science and technology)

Parallel Algorithms for Switching Edges in Heterogeneous Graphs.

Science.gov (United States)

Bhuiyan, Hasanuzzaman; Khan, Maleq; Chen, Jiangzhuo; Marathe, Madhav

2017-06-01

An edge switch is an operation on a graph (or network) where two edges are selected randomly and one of their end vertices are swapped with each other. Edge switch operations have important applications in graph theory and network analysis, such as in generating random networks with a given degree sequence, modeling and analyzing dynamic networks, and in studying various dynamic phenomena over a network. The recent growth of real-world networks motivates the need for efficient parallel algorithms. The dependencies among successive edge switch operations and the requirement to keep the graph simple (i.e., no self-loops or parallel edges) as the edges are switched lead to significant challenges in designing a parallel algorithm. Addressing these challenges requires complex synchronization and communication among the processors leading to difficulties in achieving a good speedup by parallelization. In this paper, we present distributed memory parallel algorithms for switching edges in massive networks. These algorithms provide good speedup and scale well to a large number of processors. A harmonic mean speedup of 73.25 is achieved on eight different networks with 1024 processors. One of the steps in our edge switch algorithms requires the computation of multinomial random variables in parallel. This paper presents the first non-trivial parallel algorithm for the problem, achieving a speedup of 925 using 1024 processors.

Law of large numbers for the SIR model with random vertex weights on Erdős-Rényi graph

Science.gov (United States)

Xue, Xiaofeng

2017-11-01

In this paper we are concerned with the SIR model with random vertex weights on Erdős-Rényi graph G(n , p) . The Erdős-Rényi graph G(n , p) is generated from the complete graph Cn with n vertices through independently deleting each edge with probability (1 - p) . We assign i. i. d. copies of a positive r. v. ρ on each vertex as the vertex weights. For the SIR model, each vertex is in one of the three states 'susceptible', 'infective' and 'removed'. An infective vertex infects a given susceptible neighbor at rate proportional to the production of the weights of these two vertices. An infective vertex becomes removed at a constant rate. A removed vertex will never be infected again. We assume that at t = 0 there is no removed vertex and the number of infective vertices follows a Bernoulli distribution B(n , θ) . Our main result is a law of large numbers of the model. We give two deterministic functions HS(ψt) ,HV(ψt) for t ≥ 0 and show that for any t ≥ 0, HS(ψt) is the limit proportion of susceptible vertices and HV(ψt) is the limit of the mean capability of an infective vertex to infect a given susceptible neighbor at moment t as n grows to infinity.

Topological structure of dictionary graphs

International Nuclear Information System (INIS)

Fuks, Henryk; Krzeminski, Mark

2009-01-01

We investigate the topological structure of the subgraphs of dictionary graphs constructed from WordNet and Moby thesaurus data. In the process of learning a foreign language, the learner knows only a subset of all words of the language, corresponding to a subgraph of a dictionary graph. When this subgraph grows with time, its topological properties change. We introduce the notion of the pseudocore and argue that the growth of the vocabulary roughly follows decreasing pseudocore numbers-that is, one first learns words with a high pseudocore number followed by smaller pseudocores. We also propose an alternative strategy for vocabulary growth, involving decreasing core numbers as opposed to pseudocore numbers. We find that as the core or pseudocore grows in size, the clustering coefficient first decreases, then reaches a minimum and starts increasing again. The minimum occurs when the vocabulary reaches a size between 10 3 and 10 4 . A simple model exhibiting similar behavior is proposed. The model is based on a generalized geometric random graph. Possible implications for language learning are discussed.

Chromatic graph theory

CERN Document Server

Chartrand, Gary; Rosen, Kenneth H

2008-01-01

Beginning with the origin of the four color problem in 1852, the field of graph colorings has developed into one of the most popular areas of graph theory. Introducing graph theory with a coloring theme, Chromatic Graph Theory explores connections between major topics in graph theory and graph colorings as well as emerging topics. This self-contained book first presents various fundamentals of graph theory that lie outside of graph colorings, including basic terminology and results, trees and connectivity, Eulerian and Hamiltonian graphs, matchings and factorizations, and graph embeddings. The remainder of the text deals exclusively with graph colorings. It covers vertex colorings and bounds for the chromatic number, vertex colorings of graphs embedded on surfaces, and a variety of restricted vertex colorings. The authors also describe edge colorings, monochromatic and rainbow edge colorings, complete vertex colorings, several distinguishing vertex and edge colorings, and many distance-related vertex coloring...

Measurement and correlation of excess molar volumes for mixtures of 1-propanol and aromatic hydrocarbons

International Nuclear Information System (INIS)

Gahlyan, Suman; Rani, Manju; Maken, Sanjeev Kumar; Lee, Inkyu; Moon, Il

2015-01-01

Excess molar volumes (V m E ) have been measured at 303.15 K for 1-propanol+benzene or toluene or o- or m- or p-xylene mixtures using V-shape dilatometer. The V m E values, for an equimolar composition, vary in the order: benzene>toluene-m-xylene>o-xylene>p-xylene. The V m E data have been used to calculate partial molar volumes, excess partial molar volumes, and apparent molar volumes of 1-propanol and aromatic hydrocarbons over the entire range of composition. The excess volume data have also been interpreted in terms of graph-theoretical approach and Prigogine-Flory-Patterson theory (PFP). While PFP theory fails to predict the V m E values for systems with s-shaped V m E versus x 1 graph, the V m E values calculated by graph theory compare reasonably well with the corresponding experimental values. This graph theory analysis has further yielded information about the state of aggregation of pure components as well as of the mixtures

Equilibrium statistical mechanics on correlated random graphs

Science.gov (United States)

Barra, Adriano; Agliari, Elena

2011-02-01

Biological and social networks have recently attracted great attention from physicists. Among several aspects, two main ones may be stressed: a non-trivial topology of the graph describing the mutual interactions between agents and, typically, imitative, weighted, interactions. Despite such aspects being widely accepted and empirically confirmed, the schemes currently exploited in order to generate the expected topology are based on a priori assumptions and, in most cases, implement constant intensities for links. Here we propose a simple shift [-1,+1]\\to [0,+1] in the definition of patterns in a Hopfield model: a straightforward effect is the conversion of frustration into dilution. In fact, we show that by varying the bias of pattern distribution, the network topology (generated by the reciprocal affinities among agents, i.e. the Hebbian rule) crosses various well-known regimes, ranging from fully connected, to an extreme dilution scenario, then to completely disconnected. These features, as well as small-world properties, are, in this context, emergent and no longer imposed a priori. The model is throughout investigated also from a thermodynamics perspective: the Ising model defined on the resulting graph is analytically solved (at a replica symmetric level) by extending the double stochastic stability technique, and presented together with its fluctuation theory for a picture of criticality. Overall, our findings show that, at least at equilibrium, dilution (of whatever kind) simply decreases the strength of the coupling felt by the spins, but leaves the paramagnetic/ferromagnetic flavors unchanged. The main difference with respect to previous investigations is that, within our approach, replicas do not appear: instead of (multi)-overlaps as order parameters, we introduce a class of magnetizations on all the possible subgraphs belonging to the main one investigated: as a consequence, for these objects a closure for a self-consistent relation is achieved.

Equilibrium statistical mechanics on correlated random graphs

International Nuclear Information System (INIS)

Barra, Adriano; Agliari, Elena

2011-01-01

Biological and social networks have recently attracted great attention from physicists. Among several aspects, two main ones may be stressed: a non-trivial topology of the graph describing the mutual interactions between agents and, typically, imitative, weighted, interactions. Despite such aspects being widely accepted and empirically confirmed, the schemes currently exploited in order to generate the expected topology are based on a priori assumptions and, in most cases, implement constant intensities for links. Here we propose a simple shift [-1,+1]→[0,+1] in the definition of patterns in a Hopfield model: a straightforward effect is the conversion of frustration into dilution. In fact, we show that by varying the bias of pattern distribution, the network topology (generated by the reciprocal affinities among agents, i.e. the Hebbian rule) crosses various well-known regimes, ranging from fully connected, to an extreme dilution scenario, then to completely disconnected. These features, as well as small-world properties, are, in this context, emergent and no longer imposed a priori. The model is throughout investigated also from a thermodynamics perspective: the Ising model defined on the resulting graph is analytically solved (at a replica symmetric level) by extending the double stochastic stability technique, and presented together with its fluctuation theory for a picture of criticality. Overall, our findings show that, at least at equilibrium, dilution (of whatever kind) simply decreases the strength of the coupling felt by the spins, but leaves the paramagnetic/ferromagnetic flavors unchanged. The main difference with respect to previous investigations is that, within our approach, replicas do not appear: instead of (multi)-overlaps as order parameters, we introduce a class of magnetizations on all the possible subgraphs belonging to the main one investigated: as a consequence, for these objects a closure for a self-consistent relation is achieved

Comparing brain networks of different size and connectivity density using graph theory.

Directory of Open Access Journals (Sweden)

Bernadette C M van Wijk

Full Text Available Graph theory is a valuable framework to study the organization of functional and anatomical connections in the brain. Its use for comparing network topologies, however, is not without difficulties. Graph measures may be influenced by the number of nodes (N and the average degree (k of the network. The explicit form of that influence depends on the type of network topology, which is usually unknown for experimental data. Direct comparisons of graph measures between empirical networks with different N and/or k can therefore yield spurious results. We list benefits and pitfalls of various approaches that intend to overcome these difficulties. We discuss the initial graph definition of unweighted graphs via fixed thresholds, average degrees or edge densities, and the use of weighted graphs. For instance, choosing a threshold to fix N and k does eliminate size and density effects but may lead to modifications of the network by enforcing (ignoring non-significant (significant connections. Opposed to fixing N and k, graph measures are often normalized via random surrogates but, in fact, this may even increase the sensitivity to differences in N and k for the commonly used clustering coefficient and small-world index. To avoid such a bias we tried to estimate the N,k-dependence for empirical networks, which can serve to correct for size effects, if successful. We also add a number of methods used in social sciences that build on statistics of local network structures including exponential random graph models and motif counting. We show that none of the here-investigated methods allows for a reliable and fully unbiased comparison, but some perform better than others.

Graph sampling

OpenAIRE

Zhang, L.-C.; Patone, M.

2017-01-01

We synthesise the existing theory of graph sampling. We propose a formal definition of sampling in finite graphs, and provide a classification of potential graph parameters. We develop a general approach of Horvitz–Thompson estimation to T-stage snowball sampling, and present various reformulations of some common network sampling methods in the literature in terms of the outlined graph sampling theory.

Quantum walks of two interacting particles on percolation graphs

Science.gov (United States)

Siloi, Ilaria; Benedetti, Claudia; Piccinini, Enrico; Paris, Matteo G. A.; Bordone, Paolo

2017-10-01

We address the dynamics of two indistinguishable interacting particles moving on a dynamical percolation graph, i.e., a graph where the edges are independent random telegraph processes whose values jump between 0 and 1, thus mimicking percolation. The interplay between the particle interaction strength, initial state and the percolation rate determine different dynamical regimes for the walkers. We show that, whenever the walkers are initially localised within the interaction range, fast noise enhances the particle spread compared to the noiseless case.

Algorithms for Planar Graphs and Graphs in Metric Spaces

DEFF Research Database (Denmark)

Wulff-Nilsen, Christian

structural properties that can be exploited. For instance, a road network or a wire layout on a microchip is typically (near-)planar and distances in the network are often defined w.r.t. the Euclidean or the rectilinear metric. Specialized algorithms that take advantage of such properties are often orders...... of magnitude faster than the corresponding algorithms for general graphs. The first and main part of this thesis focuses on the development of efficient planar graph algorithms. The most important contributions include a faster single-source shortest path algorithm, a distance oracle with subquadratic...... for geometric graphs and graphs embedded in metric spaces. Roughly speaking, the stretch factor is a real value expressing how well a (geo-)metric graph approximates the underlying complete graph w.r.t. distances. We give improved algorithms for computing the stretch factor of a given graph and for augmenting...

Quantum centrality testing on directed graphs via P T -symmetric quantum walks

Science.gov (United States)

Izaac, J. A.; Wang, J. B.; Abbott, P. C.; Ma, X. S.

2017-09-01

Various quantum-walk-based algorithms have been proposed to analyze and rank the centrality of graph vertices. However, issues arise when working with directed graphs: the resulting non-Hermitian Hamiltonian leads to nonunitary dynamics, and the total probability of the quantum walker is no longer conserved. In this paper, we discuss a method for simulating directed graphs using P T -symmetric quantum walks, allowing probability-conserving nonunitary evolution. This method is equivalent to mapping the directed graph to an undirected, yet weighted, complete graph over the same vertex set, and can be extended to cover interdependent networks of directed graphs. Previous work has shown centrality measures based on the continuous-time quantum walk provide an eigenvectorlike quantum centrality; using the P T -symmetric framework, we extend these centrality algorithms to directed graphs with a significantly reduced Hilbert space compared to previous proposals. In certain cases, this centrality measure provides an advantage over classical algorithms used in network analysis, for example, by breaking vertex rank degeneracy. Finally, we perform a statistical analysis over ensembles of random graphs, and show strong agreement with the classical PageRank measure on directed acyclic graphs.

Discrete probability models and methods probability on graphs and trees, Markov chains and random fields, entropy and coding

CERN Document Server

Brémaud, Pierre

2017-01-01

The emphasis in this book is placed on general models (Markov chains, random fields, random graphs), universal methods (the probabilistic method, the coupling method, the Stein-Chen method, martingale methods, the method of types) and versatile tools (Chernoff's bound, Hoeffding's inequality, Holley's inequality) whose domain of application extends far beyond the present text. Although the examples treated in the book relate to the possible applications, in the communication and computing sciences, in operations research and in physics, this book is in the first instance concerned with theory. The level of the book is that of a beginning graduate course. It is self-contained, the prerequisites consisting merely of basic calculus (series) and basic linear algebra (matrices). The reader is not assumed to be trained in probability since the first chapters give in considerable detail the background necessary to understand the rest of the book. .

Phenotypic Graphs and Evolution Unfold the Standard Genetic Code as the Optimal

Science.gov (United States)

Zamudio, Gabriel S.; José, Marco V.

2018-03-01

In this work, we explicitly consider the evolution of the Standard Genetic Code (SGC) by assuming two evolutionary stages, to wit, the primeval RNY code and two intermediate codes in between. We used network theory and graph theory to measure the connectivity of each phenotypic graph. The connectivity values are compared to the values of the codes under different randomization scenarios. An error-correcting optimal code is one in which the algebraic connectivity is minimized. We show that the SGC is optimal in regard to its robustness and error-tolerance when compared to all random codes under different assumptions.

Degree Associated Edge Reconstruction Number of Graphs with Regular Pruned Graph

Directory of Open Access Journals (Sweden)

P. Anusha Devi

2015-10-01

Full Text Available An ecard of a graph $G$ is a subgraph formed by deleting an edge. A da-ecard specifies the degree of the deleted edge along with the ecard. The degree associated edge reconstruction number of a graph $G,~dern(G,$ is the minimum number of da-ecards that uniquely determines $G.$  The adversary degree associated edge reconstruction number of a graph $G, adern(G,$ is the minimum number $k$ such that every collection of $k$ da-ecards of $G$ uniquely determines $G.$ The maximal subgraph without end vertices of a graph $G$ which is not a tree is the pruned graph of $G.$ It is shown that $dern$ of complete multipartite graphs and some connected graphs with regular pruned graph is $1$ or $2.$ We also determine $dern$ and $adern$ of corona product of standard graphs.

Introduction to graph theory

CERN Document Server

Trudeau, Richard J

1994-01-01

Preface1. Pure Mathematics Introduction; Euclidean Geometry as Pure Mathematics; Games; Why Study Pure Mathematics?; What's Coming; Suggested Reading2. Graphs Introduction; Sets; Paradox; Graphs; Graph diagrams; Cautions; Common Graphs; Discovery; Complements and Subgraphs; Isomorphism; Recognizing Isomorphic Graphs; Semantics The Number of Graphs Having a Given nu; Exercises; Suggested Reading3. Planar Graphs Introduction; UG, K subscript 5, and the Jordan Curve Theorem; Are there More Nonplanar Graphs?; Expansions; Kuratowski's Theorem; Determining Whether a Graph is Planar or

Measurement and correlation of excess molar volumes for mixtures of 1-propanol and aromatic hydrocarbons

Energy Technology Data Exchange (ETDEWEB)

Gahlyan, Suman; Rani, Manju; Maken, Sanjeev Kumar [Deenbandhu Chhotu Ram University of Science and Technology, Murthal (India); Lee, Inkyu; Moon, Il [Yonsei University, Seoul (Korea, Republic of)

2015-01-15

Excess molar volumes (V{sub m}{sup E} ) have been measured at 303.15 K for 1-propanol+benzene or toluene or o- or m- or p-xylene mixtures using V-shape dilatometer. The V{sub m}{sup E} values, for an equimolar composition, vary in the order: benzene>toluene-m-xylene>o-xylene>p-xylene. The V{sub m}{sup E} data have been used to calculate partial molar volumes, excess partial molar volumes, and apparent molar volumes of 1-propanol and aromatic hydrocarbons over the entire range of composition. The excess volume data have also been interpreted in terms of graph-theoretical approach and Prigogine-Flory-Patterson theory (PFP). While PFP theory fails to predict the V{sub m}{sup E} values for systems with s-shaped V{sub m}{sup E} versus x{sub 1} graph, the V{sub m}{sup E} values calculated by graph theory compare reasonably well with the corresponding experimental values. This graph theory analysis has further yielded information about the state of aggregation of pure components as well as of the mixtures.

Graph Theory. 2. Vertex Descriptors and Graph Coloring

Directory of Open Access Journals (Sweden)

Lorentz JÄNTSCHI

2002-12-01

Full Text Available This original work presents the construction of a set of ten sequence matrices and their applications for ordering vertices in graphs. For every sequence matrix three ordering criteria are applied: lexicographic ordering, based on strings of numbers, corresponding to every vertex, extracted as rows from sequence matrices; ordering by the sum of path lengths from a given vertex; and ordering by the sum of paths, starting from a given vertex. We also examine a graph that has different orderings for the above criteria. We then proceed to demonstrate that every criterion induced its own partition of graph vertex. We propose the following theoretical result: both LAVS and LVDS criteria generate identical partitioning of vertices in any graph. Finally, a coloring of graph vertices according to introduced ordering criteria was proposed.

On an edge partition and root graphs of some classes of line graphs

Directory of Open Access Journals (Sweden)

K Pravas

2017-04-01

Full Text Available The Gallai and the anti-Gallai graphs of a graph $G$ are complementary pairs of spanning subgraphs of the line graph of $G$. In this paper we find some structural relations between these graph classes by finding a partition of the edge set of the line graph of a graph $G$ into the edge sets of the Gallai and anti-Gallai graphs of $G$. Based on this, an optimal algorithm to find the root graph of a line graph is obtained. Moreover, root graphs of diameter-maximal, distance-hereditary, Ptolemaic and chordal graphs are also discussed.

Graphs and matrices

CERN Document Server

Bapat, Ravindra B

2014-01-01

This new edition illustrates the power of linear algebra in the study of graphs. The emphasis on matrix techniques is greater than in other texts on algebraic graph theory. Important matrices associated with graphs (for example, incidence, adjacency and Laplacian matrices) are treated in detail. Presenting a useful overview of selected topics in algebraic graph theory, early chapters of the text focus on regular graphs, algebraic connectivity, the distance matrix of a tree, and its generalized version for arbitrary graphs, known as the resistance matrix. Coverage of later topics include Laplacian eigenvalues of threshold graphs, the positive definite completion problem and matrix games based on a graph. Such an extensive coverage of the subject area provides a welcome prompt for further exploration. The inclusion of exercises enables practical learning throughout the book. In the new edition, a new chapter is added on the line graph of a tree, while some results in Chapter 6 on Perron-Frobenius theory are reo...

Learning molecular energies using localized graph kernels

Science.gov (United States)

Ferré, Grégoire; Haut, Terry; Barros, Kipton

2017-03-01

Recent machine learning methods make it possible to model potential energy of atomic configurations with chemical-level accuracy (as calculated from ab initio calculations) and at speeds suitable for molecular dynamics simulation. Best performance is achieved when the known physical constraints are encoded in the machine learning models. For example, the atomic energy is invariant under global translations and rotations; it is also invariant to permutations of same-species atoms. Although simple to state, these symmetries are complicated to encode into machine learning algorithms. In this paper, we present a machine learning approach based on graph theory that naturally incorporates translation, rotation, and permutation symmetries. Specifically, we use a random walk graph kernel to measure the similarity of two adjacency matrices, each of which represents a local atomic environment. This Graph Approximated Energy (GRAPE) approach is flexible and admits many possible extensions. We benchmark a simple version of GRAPE by predicting atomization energies on a standard dataset of organic molecules.

Chaotic Traversal (CHAT): Very Large Graphs Traversal Using Chaotic Dynamics

Science.gov (United States)

Changaival, Boonyarit; Rosalie, Martin; Danoy, Grégoire; Lavangnananda, Kittichai; Bouvry, Pascal

2017-12-01

Graph Traversal algorithms can find their applications in various fields such as routing problems, natural language processing or even database querying. The exploration can be considered as a first stepping stone into knowledge extraction from the graph which is now a popular topic. Classical solutions such as Breadth First Search (BFS) and Depth First Search (DFS) require huge amounts of memory for exploring very large graphs. In this research, we present a novel memoryless graph traversal algorithm, Chaotic Traversal (CHAT) which integrates chaotic dynamics to traverse large unknown graphs via the Lozi map and the Rössler system. To compare various dynamics effects on our algorithm, we present an original way to perform the exploration of a parameter space using a bifurcation diagram with respect to the topological structure of attractors. The resulting algorithm is an efficient and nonresource demanding algorithm, and is therefore very suitable for partial traversal of very large and/or unknown environment graphs. CHAT performance using Lozi map is proven superior than the, commonly known, Random Walk, in terms of number of nodes visited (coverage percentage) and computation time where the environment is unknown and memory usage is restricted.

Graphs cospectral with a friendship graph or its complement

Directory of Open Access Journals (Sweden)

Alireza Abdollahi

2013-12-01

Full Text Available Let $n$ be any positive integer and let $F_n$ be the friendship (or Dutch windmill graph with $2n+1$ vertices and $3n$ edges. Here we study graphs with the same adjacency spectrum as the $F_n$. Two graphs are called cospectral if the eigenvalues multiset of their adjacency matrices are the same. Let $G$ be a graph cospectral with $F_n$. Here we prove that if $G$ has no cycle of length $4$ or $5$, then $Gcong F_n$. Moreover if $G$ is connected and planar then $Gcong F_n$.All but one of connected components of $G$ are isomorphic to $K_2$.The complement $overline{F_n}$ of the friendship graph is determined by its adjacency eigenvalues, that is, if $overline{F_n}$ is cospectral with a graph $H$, then $Hcong overline{F_n}$.

MixtureTree annotator: a program for automatic colorization and visual annotation of MixtureTree.

Directory of Open Access Journals (Sweden)

Shu-Chuan Chen

Full Text Available The MixtureTree Annotator, written in JAVA, allows the user to automatically color any phylogenetic tree in Newick format generated from any phylogeny reconstruction program and output the Nexus file. By providing the ability to automatically color the tree by sequence name, the MixtureTree Annotator provides a unique advantage over any other programs which perform a similar function. In addition, the MixtureTree Annotator is the only package that can efficiently annotate the output produced by MixtureTree with mutation information and coalescent time information. In order to visualize the resulting output file, a modified version of FigTree is used. Certain popular methods, which lack good built-in visualization tools, for example, MEGA, Mesquite, PHY-FI, TreeView, treeGraph and Geneious, may give results with human errors due to either manually adding colors to each node or with other limitations, for example only using color based on a number, such as branch length, or by taxonomy. In addition to allowing the user to automatically color any given Newick tree by sequence name, the MixtureTree Annotator is the only method that allows the user to automatically annotate the resulting tree created by the MixtureTree program. The MixtureTree Annotator is fast and easy-to-use, while still allowing the user full control over the coloring and annotating process.

Topics in graph theory graphs and their Cartesian product

CERN Document Server

Imrich, Wilfried; Rall, Douglas F

2008-01-01

From specialists in the field, you will learn about interesting connections and recent developments in the field of graph theory by looking in particular at Cartesian products-arguably the most important of the four standard graph products. Many new results in this area appear for the first time in print in this book. Written in an accessible way, this book can be used for personal study in advanced applications of graph theory or for an advanced graph theory course.

Study of Chromatic parameters of Line, Total, Middle graphs and Graph operators of Bipartite graph

Science.gov (United States)

Nagarathinam, R.; Parvathi, N.

2018-04-01

Chromatic parameters have been explored on the basis of graph coloring process in which a couple of adjacent nodes receives different colors. But the Grundy and b-coloring executes maximum colors under certain restrictions. In this paper, Chromatic, b-chromatic and Grundy number of some graph operators of bipartite graph has been investigat

Handbook of graph grammars and computing by graph transformation

CERN Document Server

Engels, G; Kreowski, H J; Rozenberg, G

1999-01-01

Graph grammars originated in the late 60s, motivated by considerations about pattern recognition and compiler construction. Since then, the list of areas which have interacted with the development of graph grammars has grown quite impressively. Besides the aforementioned areas, it includes software specification and development, VLSI layout schemes, database design, modeling of concurrent systems, massively parallel computer architectures, logic programming, computer animation, developmental biology, music composition, visual languages, and many others.The area of graph grammars and graph tran

Dynamics of Nearest-Neighbour Competitions on Graphs

Science.gov (United States)

Rador, Tonguç

2017-10-01

Considering a collection of agents representing the vertices of a graph endowed with integer points, we study the asymptotic dynamics of the rate of the increase of their points according to a very simple rule: we randomly pick an an edge from the graph which unambiguously defines two agents we give a point the the agent with larger point with probability p and to the lagger with probability q such that p+q=1. The model we present is the most general version of the nearest-neighbour competition model introduced by Ben-Naim, Vazquez and Redner. We show that the model combines aspects of hyperbolic partial differential equations—as that of a conservation law—graph colouring and hyperplane arrangements. We discuss the properties of the model for general graphs but we confine in depth study to d-dimensional tori. We present a detailed study for the ring graph, which includes a chemical potential approximation to calculate all its statistics that gives rather accurate results. The two-dimensional torus, not studied in depth as the ring, is shown to possess critical behaviour in that the asymptotic speeds arrange themselves in two-coloured islands separated by borders of three other colours and the size of the islands obey power law distribution. We also show that in the large d limit the d-dimensional torus shows inverse sine law for the distribution of asymptotic speeds.

Challenges in modelling the random structure correctly in growth mixture models and the impact this has on model mixtures.

Science.gov (United States)

Gilthorpe, M S; Dahly, D L; Tu, Y K; Kubzansky, L D; Goodman, E

2014-06-01

Lifecourse trajectories of clinical or anthropological attributes are useful for identifying how our early-life experiences influence later-life morbidity and mortality. Researchers often use growth mixture models (GMMs) to estimate such phenomena. It is common to place constrains on the random part of the GMM to improve parsimony or to aid convergence, but this can lead to an autoregressive structure that distorts the nature of the mixtures and subsequent model interpretation. This is especially true if changes in the outcome within individuals are gradual compared with the magnitude of differences between individuals. This is not widely appreciated, nor is its impact well understood. Using repeat measures of body mass index (BMI) for 1528 US adolescents, we estimated GMMs that required variance-covariance constraints to attain convergence. We contrasted constrained models with and without an autocorrelation structure to assess the impact this had on the ideal number of latent classes, their size and composition. We also contrasted model options using simulations. When the GMM variance-covariance structure was constrained, a within-class autocorrelation structure emerged. When not modelled explicitly, this led to poorer model fit and models that differed substantially in the ideal number of latent classes, as well as class size and composition. Failure to carefully consider the random structure of data within a GMM framework may lead to erroneous model inferences, especially for outcomes with greater within-person than between-person homogeneity, such as BMI. It is crucial to reflect on the underlying data generation processes when building such models.

Discrete Mathematics - Special Issue: Graph Theory - dedicated to Carsten Thomassen on his 60th birthday

DEFF Research Database (Denmark)

2011-01-01

Carsten Thomassen belongs to the worlds's absolute top graph theorists, and to the world's top mathematicians in general. The special issue is a rather somewhat random collection of good papers in graph theory, by many different authors, dedicated to Carsten Thomassen on his 60th birthday. Guest ...

Optimizing spread dynamics on graphs by message passing

International Nuclear Information System (INIS)

Altarelli, F; Braunstein, A; Dall’Asta, L; Zecchina, R

2013-01-01

Cascade processes are responsible for many important phenomena in natural and social sciences. Simple models of irreversible dynamics on graphs, in which nodes activate depending on the state of their neighbors, have been successfully applied to describe cascades in a large variety of contexts. Over the past decades, much effort has been devoted to understanding the typical behavior of the cascades arising from initial conditions extracted at random from some given ensemble. However, the problem of optimizing the trajectory of the system, i.e. of identifying appropriate initial conditions to maximize (or minimize) the final number of active nodes, is still considered to be practically intractable, with the only exception being models that satisfy a sort of diminishing returns property called submodularity. Submodular models can be approximately solved by means of greedy strategies, but by definition they lack cooperative characteristics which are fundamental in many real systems. Here we introduce an efficient algorithm based on statistical physics for the optimization of trajectories in cascade processes on graphs. We show that for a wide class of irreversible dynamics, even in the absence of submodularity, the spread optimization problem can be solved efficiently on large networks. Analytic and algorithmic results on random graphs are complemented by the solution of the spread maximization problem on a real-world network (the Epinions consumer reviews network). (paper)

Optimizing spread dynamics on graphs by message passing

Science.gov (United States)

Altarelli, F.; Braunstein, A.; Dall'Asta, L.; Zecchina, R.

2013-09-01

Cascade processes are responsible for many important phenomena in natural and social sciences. Simple models of irreversible dynamics on graphs, in which nodes activate depending on the state of their neighbors, have been successfully applied to describe cascades in a large variety of contexts. Over the past decades, much effort has been devoted to understanding the typical behavior of the cascades arising from initial conditions extracted at random from some given ensemble. However, the problem of optimizing the trajectory of the system, i.e. of identifying appropriate initial conditions to maximize (or minimize) the final number of active nodes, is still considered to be practically intractable, with the only exception being models that satisfy a sort of diminishing returns property called submodularity. Submodular models can be approximately solved by means of greedy strategies, but by definition they lack cooperative characteristics which are fundamental in many real systems. Here we introduce an efficient algorithm based on statistical physics for the optimization of trajectories in cascade processes on graphs. We show that for a wide class of irreversible dynamics, even in the absence of submodularity, the spread optimization problem can be solved efficiently on large networks. Analytic and algorithmic results on random graphs are complemented by the solution of the spread maximization problem on a real-world network (the Epinions consumer reviews network).

Maximum-entropy networks pattern detection, network reconstruction and graph combinatorics

CERN Document Server

Squartini, Tiziano

2017-01-01

This book is an introduction to maximum-entropy models of random graphs with given topological properties and their applications. Its original contribution is the reformulation of many seemingly different problems in the study of both real networks and graph theory within the unified framework of maximum entropy. Particular emphasis is put on the detection of structural patterns in real networks, on the reconstruction of the properties of networks from partial information, and on the enumeration and sampling of graphs with given properties.  After a first introductory chapter explaining the motivation, focus, aim and message of the book, chapter 2 introduces the formal construction of maximum-entropy ensembles of graphs with local topological constraints. Chapter 3 focuses on the problem of pattern detection in real networks and provides a powerful way to disentangle nontrivial higher-order structural features from those that can be traced back to simpler local constraints. Chapter 4 focuses on the problem o...

A simple method for finding the scattering coefficients of quantum graphs

International Nuclear Information System (INIS)

Cottrell, Seth S.

2015-01-01

Quantum walks are roughly analogous to classical random walks, and similar to classical walks they have been used to find new (quantum) algorithms. When studying the behavior of large graphs or combinations of graphs, it is useful to find the response of a subgraph to signals of different frequencies. In doing so, we can replace an entire subgraph with a single vertex with variable scattering coefficients. In this paper, a simple technique for quickly finding the scattering coefficients of any discrete-time quantum graph will be presented. These scattering coefficients can be expressed entirely in terms of the characteristic polynomial of the graph’s time step operator. This is a marked improvement over previous techniques which have traditionally required finding eigenstates for a given eigenvalue, which is far more computationally costly. With the scattering coefficients we can easily derive the “impulse response” which is the key to predicting the response of a graph to any signal. This gives us a powerful set of tools for rapidly understanding the behavior of graphs or for reducing a large graph into its constituent subgraphs regardless of how they are connected

Centrosymmetric Graphs And A Lower Bound For Graph Energy Of Fullerenes

Directory of Open Access Journals (Sweden)

Katona Gyula Y.

2014-11-01

Full Text Available The energy of a molecular graph G is defined as the summation of the absolute values of the eigenvalues of adjacency matrix of a graph G. In this paper, an infinite class of fullerene graphs with 10n vertices, n ≥ 2, is considered. By proving centrosymmetricity of the adjacency matrix of these fullerene graphs, a lower bound for its energy is given. Our method is general and can be extended to other class of fullerene graphs.

Graphs and Homomorphisms

CERN Document Server

Hell, Pavol

2004-01-01

This is a book about graph homomorphisms. Graph theory is now an established discipline but the study of graph homomorphisms has only recently begun to gain wide acceptance and interest. The subject gives a useful perspective in areas such as graph reconstruction, products, fractional and circular colourings, and has applications in complexity theory, artificial intelligence, telecommunication, and, most recently, statistical physics.Based on the authors' lecture notes for graduate courses, this book can be used as a textbook for a second course in graph theory at 4th year or master's level an

Decomposing Oriented Graphs into Six Locally Irregular Oriented Graphs

DEFF Research Database (Denmark)

Bensmail, Julien; Renault, Gabriel

2016-01-01

An undirected graph G is locally irregular if every two of its adjacent vertices have distinct degrees. We say that G is decomposable into k locally irregular graphs if there exists a partition E1∪E2∪⋯∪Ek of the edge set E(G) such that each Ei induces a locally irregular graph. It was recently co...

Non-heuristic reduction of the graph in graph-cut optimization

International Nuclear Information System (INIS)

Malgouyres, François; Lermé, Nicolas

2012-01-01

During the last ten years, graph cuts had a growing impact in shape optimization. In particular, they are commonly used in applications of shape optimization such as image processing, computer vision and computer graphics. Their success is due to their ability to efficiently solve (apparently) difficult shape optimization problems which typically involve the perimeter of the shape. Nevertheless, solving problems with a large number of variables remains computationally expensive and requires a high memory usage since underlying graphs sometimes involve billion of nodes and even more edges. Several strategies have been proposed in the literature to improve graph-cuts in this regards. In this paper, we give a formal statement which expresses that a simple and local test performed on every node before its construction permits to avoid the construction of useless nodes for the graphs typically encountered in image processing and vision. A useless node is such that the value of the maximum flow in the graph does not change when removing the node from the graph. Such a test therefore permits to limit the construction of the graph to a band of useful nodes surrounding the final cut.

Graph embedding with rich information through heterogeneous graph

KAUST Repository

Sun, Guolei

2017-01-01

Graph embedding, aiming to learn low-dimensional representations for nodes in graphs, has attracted increasing attention due to its critical application including node classification, link prediction and clustering in social network analysis. Most

Benchmarking Measures of Network Controllability on Canonical Graph Models

Science.gov (United States)

Wu-Yan, Elena; Betzel, Richard F.; Tang, Evelyn; Gu, Shi; Pasqualetti, Fabio; Bassett, Danielle S.

2018-03-01

The control of networked dynamical systems opens the possibility for new discoveries and therapies in systems biology and neuroscience. Recent theoretical advances provide candidate mechanisms by which a system can be driven from one pre-specified state to another, and computational approaches provide tools to test those mechanisms in real-world systems. Despite already having been applied to study network systems in biology and neuroscience, the practical performance of these tools and associated measures on simple networks with pre-specified structure has yet to be assessed. Here, we study the behavior of four control metrics (global, average, modal, and boundary controllability) on eight canonical graphs (including Erdős-Rényi, regular, small-world, random geometric, Barábasi-Albert preferential attachment, and several modular networks) with different edge weighting schemes (Gaussian, power-law, and two nonparametric distributions from brain networks, as examples of real-world systems). We observe that differences in global controllability across graph models are more salient when edge weight distributions are heavy-tailed as opposed to normal. In contrast, differences in average, modal, and boundary controllability across graph models (as well as across nodes in the graph) are more salient when edge weight distributions are less heavy-tailed. Across graph models and edge weighting schemes, average and modal controllability are negatively correlated with one another across nodes; yet, across graph instances, the relation between average and modal controllability can be positive, negative, or nonsignificant. Collectively, these findings demonstrate that controllability statistics (and their relations) differ across graphs with different topologies and that these differences can be muted or accentuated by differences in the edge weight distributions. More generally, our numerical studies motivate future analytical efforts to better understand the mathematical

Graphing trillions of triangles.

Science.gov (United States)

Burkhardt, Paul

2017-07-01

The increasing size of Big Data is often heralded but how data are transformed and represented is also profoundly important to knowledge discovery, and this is exemplified in Big Graph analytics. Much attention has been placed on the scale of the input graph but the product of a graph algorithm can be many times larger than the input. This is true for many graph problems, such as listing all triangles in a graph. Enabling scalable graph exploration for Big Graphs requires new approaches to algorithms, architectures, and visual analytics. A brief tutorial is given to aid the argument for thoughtful representation of data in the context of graph analysis. Then a new algebraic method to reduce the arithmetic operations in counting and listing triangles in graphs is introduced. Additionally, a scalable triangle listing algorithm in the MapReduce model will be presented followed by a description of the experiments with that algorithm that led to the current largest and fastest triangle listing benchmarks to date. Finally, a method for identifying triangles in new visual graph exploration technologies is proposed.

Adaptive Graph Convolutional Neural Networks

OpenAIRE

Li, Ruoyu; Wang, Sheng; Zhu, Feiyun; Huang, Junzhou

2018-01-01

Graph Convolutional Neural Networks (Graph CNNs) are generalizations of classical CNNs to handle graph data such as molecular data, point could and social networks. Current filters in graph CNNs are built for fixed and shared graph structure. However, for most real data, the graph structures varies in both size and connectivity. The paper proposes a generalized and flexible graph CNN taking data of arbitrary graph structure as input. In that way a task-driven adaptive graph is learned for eac...

Optimal mixture experiments

CERN Document Server

Sinha, B K; Pal, Manisha; Das, P

2014-01-01

The book dwells mainly on the optimality aspects of mixture designs. As mixture models are a special case of regression models, a general discussion on regression designs has been presented, which includes topics like continuous designs, de la Garza phenomenon, Loewner order domination, Equivalence theorems for different optimality criteria and standard optimality results for single variable polynomial regression and multivariate linear and quadratic regression models. This is followed by a review of the available literature on estimation of parameters in mixture models. Based on recent research findings, the volume also introduces optimal mixture designs for estimation of optimum mixing proportions in different mixture models, which include Scheffé’s quadratic model, Darroch-Waller model, log- contrast model, mixture-amount models, random coefficient models and multi-response model.  Robust mixture designs and mixture designs in blocks have been also reviewed. Moreover, some applications of mixture desig...

Spectra of sparse random matrices

International Nuclear Information System (INIS)

Kuehn, Reimer

2008-01-01

We compute the spectral density for ensembles of sparse symmetric random matrices using replica. Our formulation of the replica-symmetric ansatz shares the symmetries of that suggested in a seminal paper by Rodgers and Bray (symmetry with respect to permutation of replica and rotation symmetry in the space of replica), but uses a different representation in terms of superpositions of Gaussians. It gives rise to a pair of integral equations which can be solved by a stochastic population-dynamics algorithm. Remarkably our representation allows us to identify pure-point contributions to the spectral density related to the existence of normalizable eigenstates. Our approach is not restricted to matrices defined on graphs with Poissonian degree distribution. Matrices defined on regular random graphs or on scale-free graphs, are easily handled. We also look at matrices with row constraints such as discrete graph Laplacians. Our approach naturally allows us to unfold the total density of states into contributions coming from vertices of different local coordinations and an example of such an unfolding is presented. Our results are well corroborated by numerical diagonalization studies of large finite random matrices

Asymptote Misconception on Graphing Functions: Does Graphing Software Resolve It?

Directory of Open Access Journals (Sweden)

Mehmet Fatih Öçal

2017-01-01

Full Text Available Graphing function is an important issue in mathematics education due to its use in various areas of mathematics and its potential roles for students to enhance learning mathematics. The use of some graphing software assists students’ learning during graphing functions. However, the display of graphs of functions that students sketched by hand may be relatively different when compared to the correct forms sketched using graphing software. The possible misleading effects of this situation brought a discussion of a misconception (asymptote misconception on graphing functions. The purpose of this study is two- fold. First of all, this study investigated whether using graphing software (GeoGebra in this case helps students to determine and resolve this misconception in calculus classrooms. Second, the reasons for this misconception are sought. The multiple case study was utilized in this study. University students in two calculus classrooms who received instructions with (35 students or without GeoGebra assisted instructions (32 students were compared according to whether they fell into this misconception on graphing basic functions (1/x, lnx, ex. In addition, students were interviewed to reveal the reasons behind this misconception. Data were analyzed by means of descriptive and content analysis methods. The findings indicated that those who received GeoGebra assisted instruction were better in resolving it. In addition, the reasons behind this misconception were found to be teacher-based, exam-based and some other factors.

X-Graphs: Language and Algorithms for Heterogeneous Graph Streams

Science.gov (United States)

2017-09-01

are widely used by academia and industry. 15. SUBJECT TERMS Data Analytics, Graph Analytics, High-Performance Computing 16. SECURITY CLASSIFICATION...form the core of the DeepDive Knowledge Construction System. 2 INTRODUCTION The goal of the X-Graphs project was to develop computational techniques...memory multicore machine. Ringo is based on Snap.py and SNAP, and uses Python . Ringo now allows the integration of Delite DSL Framework Graph

On the sizes of expander graphs and minimum distances of graph codes

DEFF Research Database (Denmark)

Høholdt, Tom; Justesen, Jørn

2014-01-01

We give lower bounds for the minimum distances of graph codes based on expander graphs. The bounds depend only on the second eigenvalue of the graph and the parameters of the component codes. We also give an upper bound on the size of a degree regular graph with given second eigenvalue....

Similarity Measure of Graphs

Directory of Open Access Journals (Sweden)

Amine Labriji

2017-07-01

Full Text Available The topic of identifying the similarity of graphs was considered as highly recommended research field in the Web semantic, artificial intelligence, the shape recognition and information research. One of the fundamental problems of graph databases is finding similar graphs to a graph query. Existing approaches dealing with this problem are usually based on the nodes and arcs of the two graphs, regardless of parental semantic links. For instance, a common connection is not identified as being part of the similarity of two graphs in cases like two graphs without common concepts, the measure of similarity based on the union of two graphs, or the one based on the notion of maximum common sub-graph (SCM, or the distance of edition of graphs. This leads to an inadequate situation in the context of information research. To overcome this problem, we suggest a new measure of similarity between graphs, based on the similarity measure of Wu and Palmer. We have shown that this new measure satisfies the properties of a measure of similarities and we applied this new measure on examples. The results show that our measure provides a run time with a gain of time compared to existing approaches. In addition, we compared the relevance of the similarity values obtained, it appears that this new graphs measure is advantageous and  offers a contribution to solving the problem mentioned above.

Spectra of Graphs

NARCIS (Netherlands)

Brouwer, A.E.; Haemers, W.H.

2012-01-01

This book gives an elementary treatment of the basic material about graph spectra, both for ordinary, and Laplace and Seidel spectra. The text progresses systematically, by covering standard topics before presenting some new material on trees, strongly regular graphs, two-graphs, association

Pattern graph rewrite systems

Directory of Open Access Journals (Sweden)

Aleks Kissinger

2014-03-01

Full Text Available String diagrams are a powerful tool for reasoning about physical processes, logic circuits, tensor networks, and many other compositional structures. Dixon, Duncan and Kissinger introduced string graphs, which are a combinatoric representations of string diagrams, amenable to automated reasoning about diagrammatic theories via graph rewrite systems. In this extended abstract, we show how the power of such rewrite systems can be greatly extended by introducing pattern graphs, which provide a means of expressing infinite families of rewrite rules where certain marked subgraphs, called !-boxes ("bang boxes", on both sides of a rule can be copied any number of times or removed. After reviewing the string graph formalism, we show how string graphs can be extended to pattern graphs and how pattern graphs and pattern rewrite rules can be instantiated to concrete string graphs and rewrite rules. We then provide examples demonstrating the expressive power of pattern graphs and how they can be applied to study interacting algebraic structures that are central to categorical quantum mechanics.

Information extraction and knowledge graph construction from geoscience literature

Science.gov (United States)

Wang, Chengbin; Ma, Xiaogang; Chen, Jianguo; Chen, Jingwen

2018-03-01

Geoscience literature published online is an important part of open data, and brings both challenges and opportunities for data analysis. Compared with studies of numerical geoscience data, there are limited works on information extraction and knowledge discovery from textual geoscience data. This paper presents a workflow and a few empirical case studies for that topic, with a focus on documents written in Chinese. First, we set up a hybrid corpus combining the generic and geology terms from geology dictionaries to train Chinese word segmentation rules of the Conditional Random Fields model. Second, we used the word segmentation rules to parse documents into individual words, and removed the stop-words from the segmentation results to get a corpus constituted of content-words. Third, we used a statistical method to analyze the semantic links between content-words, and we selected the chord and bigram graphs to visualize the content-words and their links as nodes and edges in a knowledge graph, respectively. The resulting graph presents a clear overview of key information in an unstructured document. This study proves the usefulness of the designed workflow, and shows the potential of leveraging natural language processing and knowledge graph technologies for geoscience.

On middle cube graphs

Directory of Open Access Journals (Sweden)

C. Dalfo

2015-10-01

Full Text Available We study a family of graphs related to the $n$-cube. The middle cube graph of parameter k is the subgraph of $Q_{2k-1}$ induced by the set of vertices whose binary representation has either $k-1$ or $k$ number of ones. The middle cube graphs can be obtained from the well-known odd graphs by doubling their vertex set. Here we study some of the properties of the middle cube graphs in the light of the theory of distance-regular graphs. In particular, we completely determine their spectra (eigenvalues and their multiplicities, and associated eigenvectors.

An Exponential Tilt Mixture Model for Time-to-Event Data to Evaluate Treatment Effect Heterogeneity in Randomized Clinical Trials.

Science.gov (United States)

Wang, Chi; Tan, Zhiqiang; Louis, Thomas A

2014-01-01

Evaluating the effect of a treatment on a time-to-event outcome is the focus of many randomized clinical trials. It is often observed that the treatment effect is heterogeneous, where only a subgroup of the patients may respond to the treatment due to some unknown mechanism such as genetic polymorphism. In this paper, we propose a semiparametric exponential tilt mixture model to estimate the proportion of patients who respond to the treatment and to assess the treatment effect. Our model is a natural extension of parametric mixture models to a semiparametric setting with a time-to-event outcome. We propose a nonparametric maximum likelihood estimation approach for inference and establish related asymptotic properties. Our method is illustrated by a randomized clinical trial on biodegradable polymer-delivered chemotherapy for malignant gliomas patients.

Graph visualization (Invited talk)

NARCIS (Netherlands)

Wijk, van J.J.; Kreveld, van M.J.; Speckmann, B.

2012-01-01

Black and white node link diagrams are the classic method to depict graphs, but these often fall short to give insight in large graphs or when attributes of nodes and edges play an important role. Graph visualization aims obtaining insight in such graphs using interactive graphical representations.

Adventures in graph theory

CERN Document Server

Joyner, W David

2017-01-01

This textbook acts as a pathway to higher mathematics by seeking and illuminating the connections between graph theory and diverse fields of mathematics, such as calculus on manifolds, group theory, algebraic curves, Fourier analysis, cryptography and other areas of combinatorics. An overview of graph theory definitions and polynomial invariants for graphs prepares the reader for the subsequent dive into the applications of graph theory. To pique the reader’s interest in areas of possible exploration, recent results in mathematics appear throughout the book, accompanied with examples of related graphs, how they arise, and what their valuable uses are. The consequences of graph theory covered by the authors are complicated and far-reaching, so topics are always exhibited in a user-friendly manner with copious graphs, exercises, and Sage code for the computation of equations. Samples of the book’s source code can be found at github.com/springer-math/adventures-in-graph-theory. The text is geared towards ad...

Information Graph Flow: A Geometric Approximation of Quantum and Statistical Systems

Science.gov (United States)

Vanchurin, Vitaly

2018-05-01

Given a quantum (or statistical) system with a very large number of degrees of freedom and a preferred tensor product factorization of the Hilbert space (or of a space of distributions) we describe how it can be approximated with a very low-dimensional field theory with geometric degrees of freedom. The geometric approximation procedure consists of three steps. The first step is to construct weighted graphs (we call information graphs) with vertices representing subsystems (e.g., qubits or random variables) and edges representing mutual information (or the flow of information) between subsystems. The second step is to deform the adjacency matrices of the information graphs to that of a (locally) low-dimensional lattice using the graph flow equations introduced in the paper. (Note that the graph flow produces very sparse adjacency matrices and thus might also be used, for example, in machine learning or network science where the task of graph sparsification is of a central importance.) The third step is to define an emergent metric and to derive an effective description of the metric and possibly other degrees of freedom. To illustrate the procedure we analyze (numerically and analytically) two information graph flows with geometric attractors (towards locally one- and two-dimensional lattices) and metric perturbations obeying a geometric flow equation. Our analysis also suggests a possible approach to (a non-perturbative) quantum gravity in which the geometry (a secondary object) emerges directly from a quantum state (a primary object) due to the flow of the information graphs.

Bipartite quantum states and random complex networks

International Nuclear Information System (INIS)

Garnerone, Silvano; Zanardi, Paolo; Giorda, Paolo

2012-01-01

We introduce a mapping between graphs and pure quantum bipartite states and show that the associated entanglement entropy conveys non-trivial information about the structure of the graph. Our primary goal is to investigate the family of random graphs known as complex networks. In the case of classical random graphs, we derive an analytic expression for the averaged entanglement entropy S-bar while for general complex networks we rely on numerics. For a large number of nodes n we find a scaling S-bar ∼c log n +g e where both the prefactor c and the sub-leading O(1) term g e are characteristic of the different classes of complex networks. In particular, g e encodes topological features of the graphs and is named network topological entropy. Our results suggest that quantum entanglement may provide a powerful tool for the analysis of large complex networks with non-trivial topological properties. (paper)

Nitrous oxide/oxygen mixture for analgesia in adult cancer patients with breakthrough pain: A randomized, double-blind controlled trial.

Science.gov (United States)

Liu, Q; Gao, L-L; Dai, Y-L; Li, Y-X; Wang, Y; Bai, C-F; Mu, G-X; Chai, X-M; Han, W-J; Zhou, L-J; Zhang, Y-J; Tang, L; Liu, J; Yu, J-Q

2018-03-01

The aim of this study was to assess the efficacy of a fixed nitrous oxide/oxygen mixture for the management of breakthrough cancer pain. A double-blind, placebo-controlled, randomized clinical trial was undertaken in the Medical ward of Tumor Hospital of General Hospital of Ningxia Medical University. 240 cancer patients with breakthrough pain were recruited and randomly received a standard pain treatment (morphine sulphate immediate release) plus a pre-prepared nitrous oxide/oxygen mixture, or the standard pain treatment plus oxygen. The primary endpoint measure was the numerical rating scale (NRS) score measured at baseline, 5 and 15 min after the beginning of treatment, and at 5 min post treatment. In all, analysis of pain score (NRS) at 5 min after the beginning of treatment shown a significant decrease in nitrous oxide/oxygen mixture treated patients with 2.8 ± 1.3 versus 5.5 ± 1.2 in controls (p nitrous oxide/oxygen was 2.0 ± 1.1 compared with 5.6 ± 1.3 for oxygen (p nitrous oxide/oxygen mixture was effective in reducing moderate to severe breakthrough pain among patients with cancer. The management of breakthrough cancer pain is always a challenge due to its temporal characteristics of rapid onset, moderate to severe in intensity, short duration (median 30-60 min). Our study find that self-administered nitrous oxide/oxygen mixture was effective in reducing moderate to severe breakthrough cancer pain. © 2017 European Pain Federation - EFIC®.

Distance-regular graphs

NARCIS (Netherlands)

van Dam, Edwin R.; Koolen, Jack H.; Tanaka, Hajime

2016-01-01

This is a survey of distance-regular graphs. We present an introduction to distance-regular graphs for the reader who is unfamiliar with the subject, and then give an overview of some developments in the area of distance-regular graphs since the monograph 'BCN'[Brouwer, A.E., Cohen, A.M., Neumaier,

Statistical mechanics of semi-supervised clustering in sparse graphs

International Nuclear Information System (INIS)

Ver Steeg, Greg; Galstyan, Aram; Allahverdyan, Armen E

2011-01-01

We theoretically study semi-supervised clustering in sparse graphs in the presence of pair-wise constraints on the cluster assignments of nodes. We focus on bi-cluster graphs and study the impact of semi-supervision for varying constraint density and overlap between the clusters. Recent results for unsupervised clustering in sparse graphs indicate that there is a critical ratio of within-cluster and between-cluster connectivities below which clusters cannot be recovered with better than random accuracy. The goal of this paper is to examine the impact of pair-wise constraints on the clustering accuracy. Our results suggest that the addition of constraints does not provide automatic improvement over the unsupervised case. When the density of the constraints is sufficiently small, their only impact is to shift the detection threshold while preserving the criticality. Conversely, if the density of (hard) constraints is above the percolation threshold, the criticality is suppressed and the detection threshold disappears

On the strong metric dimension of generalized butterfly graph, starbarbell graph, and {C}_{m}\\odot {P}_{n} graph

Science.gov (United States)

Yunia Mayasari, Ratih; Atmojo Kusmayadi, Tri

2018-04-01

Let G be a connected graph with vertex set V(G) and edge set E(G). For every pair of vertices u,v\\in V(G), the interval I[u, v] between u and v to be the collection of all vertices that belong to some shortest u ‑ v path. A vertex s\\in V(G) strongly resolves two vertices u and v if u belongs to a shortest v ‑ s path or v belongs to a shortest u ‑ s path. A vertex set S of G is a strong resolving set of G if every two distinct vertices of G are strongly resolved by some vertex of S. The strong metric basis of G is a strong resolving set with minimal cardinality. The strong metric dimension sdim(G) of a graph G is defined as the cardinality of strong metric basis. In this paper we determine the strong metric dimension of a generalized butterfly graph, starbarbell graph, and {C}mȯ {P}n graph. We obtain the strong metric dimension of generalized butterfly graph is sdim(BFn ) = 2n ‑ 2. The strong metric dimension of starbarbell graph is sdim(S{B}{m1,{m}2,\\ldots,{m}n})={\\sum }i=1n({m}i-1)-1. The strong metric dimension of {C}mȯ {P}n graph are sdim({C}mȯ {P}n)=2m-1 for m > 3 and n = 2, and sdim({C}mȯ {P}n)=2m-2 for m > 3 and n > 2.

Subgraph detection using graph signals

KAUST Repository

Chepuri, Sundeep Prabhakar

2017-03-06

In this paper we develop statistical detection theory for graph signals. In particular, given two graphs, namely, a background graph that represents an usual activity and an alternative graph that represents some unusual activity, we are interested in answering the following question: To which of the two graphs does the observed graph signal fit the best? To begin with, we assume both the graphs are known, and derive an optimal Neyman-Pearson detector. Next, we derive a suboptimal detector for the case when the alternative graph is not known. The developed theory is illustrated with numerical experiments.

Subgraph detection using graph signals

KAUST Repository

Chepuri, Sundeep Prabhakar; Leus, Geert

2017-01-01

In this paper we develop statistical detection theory for graph signals. In particular, given two graphs, namely, a background graph that represents an usual activity and an alternative graph that represents some unusual activity, we are interested in answering the following question: To which of the two graphs does the observed graph signal fit the best? To begin with, we assume both the graphs are known, and derive an optimal Neyman-Pearson detector. Next, we derive a suboptimal detector for the case when the alternative graph is not known. The developed theory is illustrated with numerical experiments.

Graph spectrum

NARCIS (Netherlands)

Brouwer, A.E.; Haemers, W.H.; Brouwer, A.E.; Haemers, W.H.

2012-01-01

This chapter presents some simple results on graph spectra.We assume the reader is familiar with elementary linear algebra and graph theory. Throughout, J will denote the all-1 matrix, and 1 is the all-1 vector.

Pragmatic Graph Rewriting Modifications

OpenAIRE

Rodgers, Peter; Vidal, Natalia

1999-01-01

We present new pragmatic constructs for easing programming in visual graph rewriting programming languages. The first is a modification to the rewriting process for nodes the host graph, where nodes specified as 'Once Only' in the LHS of a rewrite match at most once with a corresponding node in the host graph. This reduces the previously common use of tags to indicate the progress of matching in the graph. The second modification controls the application of LHS graphs, where those specified a...

Simplicial complexes of graphs

CERN Document Server

Jonsson, Jakob

2008-01-01

A graph complex is a finite family of graphs closed under deletion of edges. Graph complexes show up naturally in many different areas of mathematics, including commutative algebra, geometry, and knot theory. Identifying each graph with its edge set, one may view a graph complex as a simplicial complex and hence interpret it as a geometric object. This volume examines topological properties of graph complexes, focusing on homotopy type and homology. Many of the proofs are based on Robin Forman's discrete version of Morse theory. As a byproduct, this volume also provides a loosely defined toolbox for attacking problems in topological combinatorics via discrete Morse theory. In terms of simplicity and power, arguably the most efficient tool is Forman's divide and conquer approach via decision trees; it is successfully applied to a large number of graph and digraph complexes.

The STAPL Parallel Graph Library

KAUST Repository

Harshvardhan,

2013-01-01

This paper describes the stapl Parallel Graph Library, a high-level framework that abstracts the user from data-distribution and parallelism details and allows them to concentrate on parallel graph algorithm development. It includes a customizable distributed graph container and a collection of commonly used parallel graph algorithms. The library introduces pGraph pViews that separate algorithm design from the container implementation. It supports three graph processing algorithmic paradigms, level-synchronous, asynchronous and coarse-grained, and provides common graph algorithms based on them. Experimental results demonstrate improved scalability in performance and data size over existing graph libraries on more than 16,000 cores and on internet-scale graphs containing over 16 billion vertices and 250 billion edges. © Springer-Verlag Berlin Heidelberg 2013.

Atomic Fermi-Bose mixtures in inhomogeneous and random lattices: From Fermi glass to quantum spin glass and quantum percolation

International Nuclear Information System (INIS)

Sanpera, A.; Lewenstein, M.; Kantian, A.; Sanchez-Palencia, L.; Zakrzewski, J.

2004-01-01

We investigate strongly interacting atomic Fermi-Bose mixtures in inhomogeneous and random optical lattices. We derive an effective Hamiltonian for the system and discuss its low temperature physics. We demonstrate the possibility of controlling the interactions at local level in inhomogeneous but regular lattices. Such a control leads to the achievement of Fermi glass, quantum Fermi spin-glass, and quantum percolation regimes involving bare and/or composite fermions in random lattices

Topic Model for Graph Mining.

Science.gov (United States)

Xuan, Junyu; Lu, Jie; Zhang, Guangquan; Luo, Xiangfeng

2015-12-01

Graph mining has been a popular research area because of its numerous application scenarios. Many unstructured and structured data can be represented as graphs, such as, documents, chemical molecular structures, and images. However, an issue in relation to current research on graphs is that they cannot adequately discover the topics hidden in graph-structured data which can be beneficial for both the unsupervised learning and supervised learning of the graphs. Although topic models have proved to be very successful in discovering latent topics, the standard topic models cannot be directly applied to graph-structured data due to the "bag-of-word" assumption. In this paper, an innovative graph topic model (GTM) is proposed to address this issue, which uses Bernoulli distributions to model the edges between nodes in a graph. It can, therefore, make the edges in a graph contribute to latent topic discovery and further improve the accuracy of the supervised and unsupervised learning of graphs. The experimental results on two different types of graph datasets show that the proposed GTM outperforms the latent Dirichlet allocation on classification by using the unveiled topics of these two models to represent graphs.

Modern graph theory

CERN Document Server

Bollobás, Béla

1998-01-01

The time has now come when graph theory should be part of the education of every serious student of mathematics and computer science, both for its own sake and to enhance the appreciation of mathematics as a whole. This book is an in-depth account of graph theory, written with such a student in mind; it reflects the current state of the subject and emphasizes connections with other branches of pure mathematics. The volume grew out of the author's earlier book, Graph Theory -- An Introductory Course, but its length is well over twice that of its predecessor, allowing it to reveal many exciting new developments in the subject. Recognizing that graph theory is one of several courses competing for the attention of a student, the book contains extensive descriptive passages designed to convey the flavor of the subject and to arouse interest. In addition to a modern treatment of the classical areas of graph theory such as coloring, matching, extremal theory, and algebraic graph theory, the book presents a detailed ...

A graph edit dictionary for correcting errors in roof topology graphs reconstructed from point clouds

Science.gov (United States)

Xiong, B.; Oude Elberink, S.; Vosselman, G.

2014-07-01

In the task of 3D building model reconstruction from point clouds we face the problem of recovering a roof topology graph in the presence of noise, small roof faces and low point densities. Errors in roof topology graphs will seriously affect the final modelling results. The aim of this research is to automatically correct these errors. We define the graph correction as a graph-to-graph problem, similar to the spelling correction problem (also called the string-to-string problem). The graph correction is more complex than string correction, as the graphs are 2D while strings are only 1D. We design a strategy based on a dictionary of graph edit operations to automatically identify and correct the errors in the input graph. For each type of error the graph edit dictionary stores a representative erroneous subgraph as well as the corrected version. As an erroneous roof topology graph may contain several errors, a heuristic search is applied to find the optimum sequence of graph edits to correct the errors one by one. The graph edit dictionary can be expanded to include entries needed to cope with errors that were previously not encountered. Experiments show that the dictionary with only fifteen entries already properly corrects one quarter of erroneous graphs in about 4500 buildings, and even half of the erroneous graphs in one test area, achieving as high as a 95% acceptance rate of the reconstructed models.

Introduction to quantum graphs

CERN Document Server

Berkolaiko, Gregory

2012-01-01

A "quantum graph" is a graph considered as a one-dimensional complex and equipped with a differential operator ("Hamiltonian"). Quantum graphs arise naturally as simplified models in mathematics, physics, chemistry, and engineering when one considers propagation of waves of various nature through a quasi-one-dimensional (e.g., "meso-" or "nano-scale") system that looks like a thin neighborhood of a graph. Works that currently would be classified as discussing quantum graphs have been appearing since at least the 1930s, and since then, quantum graphs techniques have been applied successfully in various areas of mathematical physics, mathematics in general and its applications. One can mention, for instance, dynamical systems theory, control theory, quantum chaos, Anderson localization, microelectronics, photonic crystals, physical chemistry, nano-sciences, superconductivity theory, etc. Quantum graphs present many non-trivial mathematical challenges, which makes them dear to a mathematician's heart. Work on qu...

Graph Generator Survey

Energy Technology Data Exchange (ETDEWEB)

Lothian, Joshua [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Powers, Sarah S. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Sullivan, Blair D. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Baker, Matthew B. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Schrock, Jonathan [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Poole, Stephen W. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

2013-10-01

The benchmarking effort within the Extreme Scale Systems Center at Oak Ridge National Laboratory seeks to provide High Performance Computing benchmarks and test suites of interest to the DoD sponsor. The work described in this report is a part of the effort focusing on graph generation. A previously developed benchmark, SystemBurn, allowed the emulation of different application behavior profiles within a single framework. To complement this effort, similar capabilities are desired for graph-centric problems. This report examines existing synthetic graph generator implementations in preparation for further study on the properties of their generated synthetic graphs.

Functions and graphs

CERN Document Server

Gelfand, I M; Shnol, E E

1969-01-01

The second in a series of systematic studies by a celebrated mathematician I. M. Gelfand and colleagues, this volume presents students with a well-illustrated sequence of problems and exercises designed to illuminate the properties of functions and graphs. Since readers do not have the benefit of a blackboard on which a teacher constructs a graph, the authors abandoned the customary use of diagrams in which only the final form of the graph appears; instead, the book's margins feature step-by-step diagrams for the complete construction of each graph. The first part of the book employs simple fu

Loose Graph Simulations

DEFF Research Database (Denmark)

Mansutti, Alessio; Miculan, Marino; Peressotti, Marco

2017-01-01

We introduce loose graph simulations (LGS), a new notion about labelled graphs which subsumes in an intuitive and natural way subgraph isomorphism (SGI), regular language pattern matching (RLPM) and graph simulation (GS). Being a unification of all these notions, LGS allows us to express directly...... also problems which are “mixed” instances of previous ones, and hence which would not fit easily in any of them. After the definition and some examples, we show that the problem of finding loose graph simulations is NP-complete, we provide formal translation of SGI, RLPM, and GS into LGSs, and we give...

SpectralNET – an application for spectral graph analysis and visualization

Directory of Open Access Journals (Sweden)

Schreiber Stuart L

2005-10-01

Full Text Available Abstract Background Graph theory provides a computational framework for modeling a variety of datasets including those emerging from genomics, proteomics, and chemical genetics. Networks of genes, proteins, small molecules, or other objects of study can be represented as graphs of nodes (vertices and interactions (edges that can carry different weights. SpectralNET is a flexible application for analyzing and visualizing these biological and chemical networks. Results Available both as a standalone .NET executable and as an ASP.NET web application, SpectralNET was designed specifically with the analysis of graph-theoretic metrics in mind, a computational task not easily accessible using currently available applications. Users can choose either to upload a network for analysis using a variety of input formats, or to have SpectralNET generate an idealized random network for comparison to a real-world dataset. Whichever graph-generation method is used, SpectralNET displays detailed information about each connected component of the graph, including graphs of degree distribution, clustering coefficient by degree, and average distance by degree. In addition, extensive information about the selected vertex is shown, including degree, clustering coefficient, various distance metrics, and the corresponding components of the adjacency, Laplacian, and normalized Laplacian eigenvectors. SpectralNET also displays several graph visualizations, including a linear dimensionality reduction for uploaded datasets (Principal Components Analysis and a non-linear dimensionality reduction that provides an elegant view of global graph structure (Laplacian eigenvectors. Conclusion SpectralNET provides an easily accessible means of analyzing graph-theoretic metrics for data modeling and dimensionality reduction. SpectralNET is publicly available as both a .NET application and an ASP.NET web application from http://chembank.broad.harvard.edu/resources/. Source code is

Neural networks for link prediction in realistic biomedical graphs: a multi-dimensional evaluation of graph embedding-based approaches.

Science.gov (United States)

Crichton, Gamal; Guo, Yufan; Pyysalo, Sampo; Korhonen, Anna

2018-05-21

Link prediction in biomedical graphs has several important applications including predicting Drug-Target Interactions (DTI), Protein-Protein Interaction (PPI) prediction and Literature-Based Discovery (LBD). It can be done using a classifier to output the probability of link formation between nodes. Recently several works have used neural networks to create node representations which allow rich inputs to neural classifiers. Preliminary works were done on this and report promising results. However they did not use realistic settings like time-slicing, evaluate performances with comprehensive metrics or explain when or why neural network methods outperform. We investigated how inputs from four node representation algorithms affect performance of a neural link predictor on random- and time-sliced biomedical graphs of real-world sizes (∼ 6 million edges) containing information relevant to DTI, PPI and LBD. We compared the performance of the neural link predictor to those of established baselines and report performance across five metrics. In random- and time-sliced experiments when the neural network methods were able to learn good node representations and there was a negligible amount of disconnected nodes, those approaches outperformed the baselines. In the smallest graph (∼ 15,000 edges) and in larger graphs with approximately 14% disconnected nodes, baselines such as Common Neighbours proved a justifiable choice for link prediction. At low recall levels (∼ 0.3) the approaches were mostly equal, but at higher recall levels across all nodes and average performance at individual nodes, neural network approaches were superior. Analysis showed that neural network methods performed well on links between nodes with no previous common neighbours; potentially the most interesting links. Additionally, while neural network methods benefit from large amounts of data, they require considerable amounts of computational resources to utilise them. Our results indicate

Effect of randomization of mixtures of butter oil and vegetable oil on absorption and lipid metabolism in rats

DEFF Research Database (Denmark)

Becker, C.; Lund, Pia; Hølmer, Gunhild Kofoed

2001-01-01

of the dietary fats compared. Data on the fate of such lipids beyond the bloodstream is rather scarce and animal model studies are needed. Aim of the study To compare the metabolism of butter oil and mixtures of butter and rapeseed oil, native or randomized, in a model. The regiospecific fatty acid distribution...... present in dietary fats was followed through absorption, chylomicron formation, and deposition in adipose tissue and in different liver lipids (triacylglycerols, phospholipids, and cholesterol esters). Methods Rats were fed for 6 weeks from weaning either butter oil (BO), a butteroil- rapeseed oil mixture...... (interesterification) of butter oil with rapeseed oil (65:35 w/w) for use as edible fat did not have any impact on the fatty acid composition beyond the chylomicron step when compared to the native mixture....

SNAP: A General Purpose Network Analysis and Graph Mining Library.

Science.gov (United States)

Leskovec, Jure; Sosič, Rok

2016-10-01

Large networks are becoming a widely used abstraction for studying complex systems in a broad set of disciplines, ranging from social network analysis to molecular biology and neuroscience. Despite an increasing need to analyze and manipulate large networks, only a limited number of tools are available for this task. Here, we describe Stanford Network Analysis Platform (SNAP), a general-purpose, high-performance system that provides easy to use, high-level operations for analysis and manipulation of large networks. We present SNAP functionality, describe its implementational details, and give performance benchmarks. SNAP has been developed for single big-memory machines and it balances the trade-off between maximum performance, compact in-memory graph representation, and the ability to handle dynamic graphs where nodes and edges are being added or removed over time. SNAP can process massive networks with hundreds of millions of nodes and billions of edges. SNAP offers over 140 different graph algorithms that can efficiently manipulate large graphs, calculate structural properties, generate regular and random graphs, and handle attributes and meta-data on nodes and edges. Besides being able to handle large graphs, an additional strength of SNAP is that networks and their attributes are fully dynamic, they can be modified during the computation at low cost. SNAP is provided as an open source library in C++ as well as a module in Python. We also describe the Stanford Large Network Dataset, a set of social and information real-world networks and datasets, which we make publicly available. The collection is a complementary resource to our SNAP software and is widely used for development and benchmarking of graph analytics algorithms.

Using Exponential Random Graph Models to Analyze the Character of Peer Relationship Networks and Their Effects on the Subjective Well-being of Adolescents.

Science.gov (United States)

Jiao, Can; Wang, Ting; Liu, Jianxin; Wu, Huanjie; Cui, Fang; Peng, Xiaozhe

2017-01-01

The influences of peer relationships on adolescent subjective well-being were investigated within the framework of social network analysis, using exponential random graph models as a methodological tool. The participants in the study were 1,279 students (678 boys and 601 girls) from nine junior middle schools in Shenzhen, China. The initial stage of the research used a peer nomination questionnaire and a subjective well-being scale (used in previous studies) to collect data on the peer relationship networks and the subjective well-being of the students. Exponential random graph models were then used to explore the relationships between students with the aim of clarifying the character of the peer relationship networks and the influence of peer relationships on subjective well being. The results showed that all the adolescent peer relationship networks in our investigation had positive reciprocal effects, positive transitivity effects and negative expansiveness effects. However, none of the relationship networks had obvious receiver effects or leaders. The adolescents in partial peer relationship networks presented similar levels of subjective well-being on three dimensions (satisfaction with life, positive affects and negative affects) though not all network friends presented these similarities. The study shows that peer networks can affect an individual's subjective well-being. However, whether similarities among adolescents are the result of social influences or social choices needs further exploration, including longitudinal studies that investigate the potential processes of subjective well-being similarities among adolescents.

Thermodynamic properties of binary mixtures of tetrahydropyran with pyridine and isomeric picolines: Excess molar volumes, excess molar enthalpies and excess isentropic compressibilities

International Nuclear Information System (INIS)

Saini, Neeti; Jangra, Sunil K.; Yadav, J.S.; Sharma, Dimple; Sharma, V.K.

2011-01-01

Research highlights: → Densities, ρ and speeds of sound, u of tetrahydropyran (i) + pyridine or α-, β- or γ-picoline (j) binary mixtures at 298.15, 303.15 and 308.15 K and excess molar enthalpies, H E of the same set of mixtures at 308.15 K have been measured as a function of composition. → The observed densities and speeds of sound values have been employed to determine excess molar volumes, V E and excess isentropic compressibilities, κ S E . → Topology of the constituents of mixtures has been utilized (Graph theory) successfully to predict V E , H E and κ S E data of the investigated mixtures. → Thermodynamic data of the various mixtures have also been analyzed in terms of Prigogine-Flory-Patterson (PFP) theory. - Abstract: Densities, ρ and speeds of sound, u of tetrahydropyran (i) + pyridine or α-, β- or γ- picoline (j) binary mixtures at 298.15, 303.15 and 308.15 K and excess molar enthalpies, H E of the same set of mixtures at 308.15 K have been measured as a function of composition using an anton Parr vibrating-tube digital density and sound analyzer (model DSA 5000) and 2-drop micro-calorimeter, respectively. The resulting density and speed of sound data of the investigated mixtures have been utilized to predict excess molar volumes, V E and excess isentropic compressibilities, κ S E . The observed data have been analyzed in terms of (i) Graph theory; (ii) Prigogine-Flory-Patterson theory. It has been observed that V E , H E and κ S E data predicted by Graph theory compare well with their experimental values.

Gaussian Mixture Random Coefficient model based framework for SHM in structures with time-dependent dynamics under uncertainty

Science.gov (United States)

Avendaño-Valencia, Luis David; Fassois, Spilios D.

2017-12-01

The problem of vibration-based damage diagnosis in structures characterized by time-dependent dynamics under significant environmental and/or operational uncertainty is considered. A stochastic framework consisting of a Gaussian Mixture Random Coefficient model of the uncertain time-dependent dynamics under each structural health state, proper estimation methods, and Bayesian or minimum distance type decision making, is postulated. The Random Coefficient (RC) time-dependent stochastic model with coefficients following a multivariate Gaussian Mixture Model (GMM) allows for significant flexibility in uncertainty representation. Certain of the model parameters are estimated via a simple procedure which is founded on the related Multiple Model (MM) concept, while the GMM weights are explicitly estimated for optimizing damage diagnostic performance. The postulated framework is demonstrated via damage detection in a simple simulated model of a quarter-car active suspension with time-dependent dynamics and considerable uncertainty on the payload. Comparisons with a simpler Gaussian RC model based method are also presented, with the postulated framework shown to be capable of offering considerable improvement in diagnostic performance.

Probabilistic generation of random networks taking into account information on motifs occurrence.

Science.gov (United States)

Bois, Frederic Y; Gayraud, Ghislaine

2015-01-01

Because of the huge number of graphs possible even with a small number of nodes, inference on network structure is known to be a challenging problem. Generating large random directed graphs with prescribed probabilities of occurrences of some meaningful patterns (motifs) is also difficult. We show how to generate such random graphs according to a formal probabilistic representation, using fast Markov chain Monte Carlo methods to sample them. As an illustration, we generate realistic graphs with several hundred nodes mimicking a gene transcription interaction network in Escherichia coli.

Tailored graph ensembles as proxies or null models for real networks II: results on directed graphs

International Nuclear Information System (INIS)

Roberts, E S; Coolen, A C C; Schlitt, T

2011-01-01

We generate new mathematical tools with which to quantify the macroscopic topological structure of large directed networks. This is achieved via a statistical mechanical analysis of constrained maximum entropy ensembles of directed random graphs with prescribed joint distributions for in- and out-degrees and prescribed degree-degree correlation functions. We calculate exact and explicit formulae for the leading orders in the system size of the Shannon entropies and complexities of these ensembles, and for information-theoretic distances. The results are applied to data on gene regulation networks.

Autoregressive Moving Average Graph Filtering

OpenAIRE

Isufi, Elvin; Loukas, Andreas; Simonetto, Andrea; Leus, Geert

2016-01-01

One of the cornerstones of the field of signal processing on graphs are graph filters, direct analogues of classical filters, but intended for signals defined on graphs. This work brings forth new insights on the distributed graph filtering problem. We design a family of autoregressive moving average (ARMA) recursions, which (i) are able to approximate any desired graph frequency response, and (ii) give exact solutions for tasks such as graph signal denoising and interpolation. The design phi...

On cyclic orthogonal double covers of circulant graphs by special infinite graphs

Directory of Open Access Journals (Sweden)

R. El-Shanawany

2017-12-01

Full Text Available In this article, a technique to construct cyclic orthogonal double covers (CODCs of regular circulant graphs by certain infinite graph classes such as complete bipartite and tripartite graphs and disjoint union of butterfly and K1,2n−10 is introduced.

Fundamentals of algebraic graph transformation

CERN Document Server

Ehrig, Hartmut; Prange, Ulrike; Taentzer, Gabriele

2006-01-01

Graphs are widely used to represent structural information in the form of objects and connections between them. Graph transformation is the rule-based manipulation of graphs, an increasingly important concept in computer science and related fields. This is the first textbook treatment of the algebraic approach to graph transformation, based on algebraic structures and category theory. Part I is an introduction to the classical case of graph and typed graph transformation. In Part II basic and advanced results are first shown for an abstract form of replacement systems, so-called adhesive high-level replacement systems based on category theory, and are then instantiated to several forms of graph and Petri net transformation systems. Part III develops typed attributed graph transformation, a technique of key relevance in the modeling of visual languages and in model transformation. Part IV contains a practical case study on model transformation and a presentation of the AGG (attributed graph grammar) tool envir...

Graph-based modelling in engineering

CERN Document Server

Rysiński, Jacek

2017-01-01

This book presents versatile, modern and creative applications of graph theory in mechanical engineering, robotics and computer networks. Topics related to mechanical engineering include e.g. machine and mechanism science, mechatronics, robotics, gearing and transmissions, design theory and production processes. The graphs treated are simple graphs, weighted and mixed graphs, bond graphs, Petri nets, logical trees etc. The authors represent several countries in Europe and America, and their contributions show how different, elegant, useful and fruitful the utilization of graphs in modelling of engineering systems can be. .

BootGraph: probabilistic fiber tractography using bootstrap algorithms and graph theory.

Science.gov (United States)

Vorburger, Robert S; Reischauer, Carolin; Boesiger, Peter

2013-02-01

Bootstrap methods have recently been introduced to diffusion-weighted magnetic resonance imaging to estimate the measurement uncertainty of ensuing diffusion parameters directly from the acquired data without the necessity to assume a noise model. These methods have been previously combined with deterministic streamline tractography algorithms to allow for the assessment of connection probabilities in the human brain. Thereby, the local noise induced disturbance in the diffusion data is accumulated additively due to the incremental progression of streamline tractography algorithms. Graph based approaches have been proposed to overcome this drawback of streamline techniques. For this reason, the bootstrap method is in the present work incorporated into a graph setup to derive a new probabilistic fiber tractography method, called BootGraph. The acquired data set is thereby converted into a weighted, undirected graph by defining a vertex in each voxel and edges between adjacent vertices. By means of the cone of uncertainty, which is derived using the wild bootstrap, a weight is thereafter assigned to each edge. Two path finding algorithms are subsequently applied to derive connection probabilities. While the first algorithm is based on the shortest path approach, the second algorithm takes all existing paths between two vertices into consideration. Tracking results are compared to an established algorithm based on the bootstrap method in combination with streamline fiber tractography and to another graph based algorithm. The BootGraph shows a very good performance in crossing situations with respect to false negatives and permits incorporating additional constraints, such as a curvature threshold. By inheriting the advantages of the bootstrap method and graph theory, the BootGraph method provides a computationally efficient and flexible probabilistic tractography setup to compute connection probability maps and virtual fiber pathways without the drawbacks of

Equity trees and graphs via information theory

Science.gov (United States)

Harré, M.; Bossomaier, T.

2010-01-01

We investigate the similarities and differences between two measures of the relationship between equities traded in financial markets. Our measures are the correlation coefficients and the mutual information. In the context of financial markets correlation coefficients are well established whereas mutual information has not previously been as well studied despite its theoretically appealing properties. We show that asset trees which are derived from either the correlation coefficients or the mutual information have a mixture of both similarities and differences at the individual equity level and at the macroscopic level. We then extend our consideration from trees to graphs using the "genus 0" condition recently introduced in order to study the networks of equities.

Artistic image analysis using graph-based learning approaches.

Science.gov (United States)

Carneiro, Gustavo

2013-08-01

We introduce a new methodology for the problem of artistic image analysis, which among other tasks, involves the automatic identification of visual classes present in an art work. In this paper, we advocate the idea that artistic image analysis must explore a graph that captures the network of artistic influences by computing the similarities in terms of appearance and manual annotation. One of the novelties of our methodology is the proposed formulation that is a principled way of combining these two similarities in a single graph. Using this graph, we show that an efficient random walk algorithm based on an inverted label propagation formulation produces more accurate annotation and retrieval results compared with the following baseline algorithms: bag of visual words, label propagation, matrix completion, and structural learning. We also show that the proposed approach leads to a more efficient inference and training procedures. This experiment is run on a database containing 988 artistic images (with 49 visual classification problems divided into a multiclass problem with 27 classes and 48 binary problems), where we show the inference and training running times, and quantitative comparisons with respect to several retrieval and annotation performance measures.

Linear game non-contextuality and Bell inequalities—a graph-theoretic approach

International Nuclear Information System (INIS)

Rosicka, M; Ramanathan, R; Gnaciński, P; Horodecki, M; Horodecki, K; Horodecki, P; Severini, S

2016-01-01

We study the classical and quantum values of a class of one- and two-party unique games, that generalizes the well-known XOR games to the case of non-binary outcomes. In the bipartite case the generalized XOR (XOR-d) games we study are a subclass of the well-known linear games. We introduce a ‘constraint graph’ associated to such a game, with the constraints defining the game represented by an edge-coloring of the graph. We use the graph-theoretic characterization to relate the task of finding equivalent games to the notion of signed graphs and switching equivalence from graph theory. We relate the problem of computing the classical value of single-party anti-correlation XOR games to finding the edge bipartization number of a graph, which is known to be MaxSNP hard, and connect the computation of the classical value of XOR-d games to the identification of specific cycles in the graph. We construct an orthogonality graph of the game from the constraint graph and study its Lovász theta number as a general upper bound on the quantum value even in the case of single-party contextual XOR-d games. XOR-d games possess appealing properties for use in device-independent applications such as randomness of the local correlated outcomes in the optimal quantum strategy. We study the possibility of obtaining quantum algebraic violation of these games, and show that no finite XOR-d game possesses the property of pseudo-telepathy leaving the frequently used chained Bell inequalities as the natural candidates for such applications. We also show this lack of pseudo-telepathy for multi-party XOR-type inequalities involving two-body correlation functions. (paper)

Linear game non-contextuality and Bell inequalities—a graph-theoretic approach

Science.gov (United States)

Rosicka, M.; Ramanathan, R.; Gnaciński, P.; Horodecki, K.; Horodecki, M.; Horodecki, P.; Severini, S.

2016-04-01

We study the classical and quantum values of a class of one- and two-party unique games, that generalizes the well-known XOR games to the case of non-binary outcomes. In the bipartite case the generalized XOR (XOR-d) games we study are a subclass of the well-known linear games. We introduce a ‘constraint graph’ associated to such a game, with the constraints defining the game represented by an edge-coloring of the graph. We use the graph-theoretic characterization to relate the task of finding equivalent games to the notion of signed graphs and switching equivalence from graph theory. We relate the problem of computing the classical value of single-party anti-correlation XOR games to finding the edge bipartization number of a graph, which is known to be MaxSNP hard, and connect the computation of the classical value of XOR-d games to the identification of specific cycles in the graph. We construct an orthogonality graph of the game from the constraint graph and study its Lovász theta number as a general upper bound on the quantum value even in the case of single-party contextual XOR-d games. XOR-d games possess appealing properties for use in device-independent applications such as randomness of the local correlated outcomes in the optimal quantum strategy. We study the possibility of obtaining quantum algebraic violation of these games, and show that no finite XOR-d game possesses the property of pseudo-telepathy leaving the frequently used chained Bell inequalities as the natural candidates for such applications. We also show this lack of pseudo-telepathy for multi-party XOR-type inequalities involving two-body correlation functions.

Equipackable graphs

DEFF Research Database (Denmark)

Vestergaard, Preben Dahl; Hartnell, Bert L.

2006-01-01

There are many results dealing with the problem of decomposing a fixed graph into isomorphic subgraphs. There has also been work on characterizing graphs with the property that one can delete the edges of a number of edge disjoint copies of the subgraph and, regardless of how that is done, the gr...

Khovanov homology of graph-links

Energy Technology Data Exchange (ETDEWEB)

Nikonov, Igor M [M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)

2012-08-31

Graph-links arise as the intersection graphs of turning chord diagrams of links. Speaking informally, graph-links provide a combinatorial description of links up to mutations. Many link invariants can be reformulated in the language of graph-links. Khovanov homology, a well-known and useful knot invariant, is defined for graph-links in this paper (in the case of the ground field of characteristic two). Bibliography: 14 titles.

On two energy-like invariants of line graphs and related graph operations

Directory of Open Access Journals (Sweden)

Xiaodan Chen

2016-02-01

Full Text Available Abstract For a simple graph G of order n, let μ 1 ≥ μ 2 ≥ ⋯ ≥ μ n = 0 $\\mu_{1}\\geq\\mu_{2}\\geq\\cdots\\geq\\mu_{n}=0$ be its Laplacian eigenvalues, and let q 1 ≥ q 2 ≥ ⋯ ≥ q n ≥ 0 $q_{1}\\geq q_{2}\\geq\\cdots\\geq q_{n}\\geq0$ be its signless Laplacian eigenvalues. The Laplacian-energy-like invariant and incidence energy of G are defined as, respectively, LEL ( G = ∑ i = 1 n − 1 μ i and IE ( G = ∑ i = 1 n q i . $$\\mathit{LEL}(G=\\sum_{i=1}^{n-1}\\sqrt{ \\mu_{i}} \\quad\\mbox{and}\\quad \\mathit {IE}(G=\\sum_{i=1}^{n} \\sqrt{q_{i}}. $$ In this paper, we present some new upper and lower bounds on LEL and IE of line graph, subdivision graph, para-line graph and total graph of a regular graph, some of which improve previously known results. The main tools we use here are the Cauchy-Schwarz inequality and the Ozeki inequality.

Refractometry for quality control of anesthetic drug mixtures.

Science.gov (United States)

Stabenow, Jennifer M; Maske, Mindy L; Vogler, George A

2006-07-01

Injectable anesthetic drugs used in rodents are often mixed and further diluted to increase the convenience and accuracy of dosing. We evaluated clinical refractometry as a simple and rapid method of quality control and mixing error detection of rodent anesthetic or analgesic mixtures. Dilutions of ketamine, xylazine, acepromazine, and buprenorphine were prepared with reagent-grade water to produce at least 4 concentration levels. The refraction of each concentration then was measured with a clinical refractometer and plotted against the percentage of stock concentration. The resulting graphs were linear and could be used to determine the concentration of single-drug dilutions or to predict the refraction of drug mixtures. We conclude that refractometry can be used to assess the concentration of dilutions of single drugs and can verify the mixing accuracy of drug combinations when the components of the mixture are known and fall within the detection range of the instrument.

Price Competition on Graphs

OpenAIRE

Adriaan R. Soetevent

2010-01-01

This paper extends Hotelling's model of price competition with quadratic transportation costs from a line to graphs. I propose an algorithm to calculate firm-level demand for any given graph, conditional on prices and firm locations. One feature of graph models of price competition is that spatial discontinuities in firm-level demand may occur. I show that the existence result of D'Aspremont et al. (1979) does not extend to simple star graphs. I conjecture that this non-existence result holds...

Price Competition on Graphs

OpenAIRE

Pim Heijnen; Adriaan Soetevent

2014-01-01

This paper extends Hotelling's model of price competition with quadratic transportation costs from a line to graphs. We derive an algorithm to calculate firm-level demand for any given graph, conditional on prices and firm locations. These graph models of price competition may lead to spatial discontinuities in firm-level demand. We show that the existence result of D'Aspremont et al. (1979) does not extend to simple star graphs and conjecture that this non-existence result holds more general...

Skew-adjacency matrices of graphs

NARCIS (Netherlands)

Cavers, M.; Cioaba, S.M.; Fallat, S.; Gregory, D.A.; Haemers, W.H.; Kirkland, S.J.; McDonald, J.J.; Tsatsomeros, M.

2012-01-01

The spectra of the skew-adjacency matrices of a graph are considered as a possible way to distinguish adjacency cospectral graphs. This leads to the following topics: graphs whose skew-adjacency matrices are all cospectral; relations between the matchings polynomial of a graph and the characteristic

Graph theory

CERN Document Server

Diestel, Reinhard

2017-01-01

This standard textbook of modern graph theory, now in its fifth edition, combines the authority of a classic with the engaging freshness of style that is the hallmark of active mathematics. It covers the core material of the subject with concise yet reliably complete proofs, while offering glimpses of more advanced methods in each field by one or two deeper results, again with proofs given in full detail. The book can be used as a reliable text for an introductory course, as a graduate text, and for self-study. From the reviews: “This outstanding book cannot be substituted with any other book on the present textbook market. It has every chance of becoming the standard textbook for graph theory.”Acta Scientiarum Mathematiciarum “Deep, clear, wonderful. This is a serious book about the heart of graph theory. It has depth and integrity. ”Persi Diaconis & Ron Graham, SIAM Review “The book has received a very enthusiastic reception, which it amply deserves. A masterly elucidation of modern graph theo...

Acyclicity in edge-colored graphs

DEFF Research Database (Denmark)

Gutin, Gregory; Jones, Mark; Sheng, Bin

2017-01-01

A walk W in edge-colored graphs is called properly colored (PC) if every pair of consecutive edges in W is of different color. We introduce and study five types of PC acyclicity in edge-colored graphs such that graphs of PC acyclicity of type i is a proper superset of graphs of acyclicity of type i......+1, i=1,2,3,4. The first three types are equivalent to the absence of PC cycles, PC closed trails, and PC closed walks, respectively. While graphs of types 1, 2 and 3 can be recognized in polynomial time, the problem of recognizing graphs of type 4 is, somewhat surprisingly, NP-hard even for 2-edge-colored...... graphs (i.e., when only two colors are used). The same problem with respect to type 5 is polynomial-time solvable for all edge-colored graphs. Using the five types, we investigate the border between intractability and tractability for the problems of finding the maximum number of internally vertex...

Graph Sampling for Covariance Estimation

KAUST Repository

Chepuri, Sundeep Prabhakar

2017-04-25

In this paper the focus is on subsampling as well as reconstructing the second-order statistics of signals residing on nodes of arbitrary undirected graphs. Second-order stationary graph signals may be obtained by graph filtering zero-mean white noise and they admit a well-defined power spectrum whose shape is determined by the frequency response of the graph filter. Estimating the graph power spectrum forms an important component of stationary graph signal processing and related inference tasks such as Wiener prediction or inpainting on graphs. The central result of this paper is that by sampling a significantly smaller subset of vertices and using simple least squares, we can reconstruct the second-order statistics of the graph signal from the subsampled observations, and more importantly, without any spectral priors. To this end, both a nonparametric approach as well as parametric approaches including moving average and autoregressive models for the graph power spectrum are considered. The results specialize for undirected circulant graphs in that the graph nodes leading to the best compression rates are given by the so-called minimal sparse rulers. A near-optimal greedy algorithm is developed to design the subsampling scheme for the non-parametric and the moving average models, whereas a particular subsampling scheme that allows linear estimation for the autoregressive model is proposed. Numerical experiments on synthetic as well as real datasets related to climatology and processing handwritten digits are provided to demonstrate the developed theory.

Price competition on graphs

NARCIS (Netherlands)

Soetevent, A.R.

2010-01-01

This paper extends Hotelling's model of price competition with quadratic transportation costs from a line to graphs. I propose an algorithm to calculate firm-level demand for any given graph, conditional on prices and firm locations. One feature of graph models of price competition is that spatial

Graphing the order of the sexes: constructing, recalling, interpreting, and putting the self in gender difference graphs.

Science.gov (United States)

Hegarty, Peter; Lemieux, Anthony F; McQueen, Grant

2010-03-01

Graphs seem to connote facts more than words or tables do. Consequently, they seem unlikely places to spot implicit sexism at work. Yet, in 6 studies (N = 741), women and men constructed (Study 1) and recalled (Study 2) gender difference graphs with men's data first, and graphed powerful groups (Study 3) and individuals (Study 4) ahead of weaker ones. Participants who interpreted graph order as evidence of author "bias" inferred that the author graphed his or her own gender group first (Study 5). Women's, but not men's, preferences to graph men first were mitigated when participants graphed a difference between themselves and an opposite-sex friend prior to graphing gender differences (Study 6). Graph production and comprehension are affected by beliefs and suppositions about the groups represented in graphs to a greater degree than cognitive models of graph comprehension or realist models of scientific thinking have yet acknowledged.

Multifractal analysis of visibility graph-based Ito-related connectivity time series.

Science.gov (United States)

Czechowski, Zbigniew; Lovallo, Michele; Telesca, Luciano

2016-02-01

In this study, we investigate multifractal properties of connectivity time series resulting from the visibility graph applied to normally distributed time series generated by the Ito equations with multiplicative power-law noise. We show that multifractality of the connectivity time series (i.e., the series of numbers of links outgoing any node) increases with the exponent of the power-law noise. The multifractality of the connectivity time series could be due to the width of connectivity degree distribution that can be related to the exit time of the associated Ito time series. Furthermore, the connectivity time series are characterized by persistence, although the original Ito time series are random; this is due to the procedure of visibility graph that, connecting the values of the time series, generates persistence but destroys most of the nonlinear correlations. Moreover, the visibility graph is sensitive for detecting wide "depressions" in input time series.

Collective Rationality in Graph Aggregation

NARCIS (Netherlands)

Endriss, U.; Grandi, U.; Schaub, T.; Friedrich, G.; O'Sullivan, B.

2014-01-01

Suppose a number of agents each provide us with a directed graph over a common set of vertices. Graph aggregation is the problem of computing a single “collective” graph that best represents the information inherent in this profile of individual graphs. We consider this aggregation problem from the

GoFFish: A Sub-Graph Centric Framework for Large-Scale Graph Analytics1

Energy Technology Data Exchange (ETDEWEB)

Simmhan, Yogesh; Kumbhare, Alok; Wickramaarachchi, Charith; Nagarkar, Soonil; Ravi, Santosh; Raghavendra, Cauligi; Prasanna, Viktor

2014-08-25

Large scale graph processing is a major research area for Big Data exploration. Vertex centric programming models like Pregel are gaining traction due to their simple abstraction that allows for scalable execution on distributed systems naturally. However, there are limitations to this approach which cause vertex centric algorithms to under-perform due to poor compute to communication overhead ratio and slow convergence of iterative superstep. In this paper we introduce GoFFish a scalable sub-graph centric framework co-designed with a distributed persistent graph storage for large scale graph analytics on commodity clusters. We introduce a sub-graph centric programming abstraction that combines the scalability of a vertex centric approach with the flexibility of shared memory sub-graph computation. We map Connected Components, SSSP and PageRank algorithms to this model to illustrate its flexibility. Further, we empirically analyze GoFFish using several real world graphs and demonstrate its significant performance improvement, orders of magnitude in some cases, compared to Apache Giraph, the leading open source vertex centric implementation. We map Connected Components, SSSP and PageRank algorithms to this model to illustrate its flexibility. Further, we empirically analyze GoFFish using several real world graphs and demonstrate its significant performance improvement, orders of magnitude in some cases, compared to Apache Giraph, the leading open source vertex centric implementation.

Graph Theory. 1. Fragmentation of Structural Graphs

Directory of Open Access Journals (Sweden)

Lorentz JÄNTSCHI

2002-12-01

Full Text Available The investigation of structural graphs has many fields of applications in engineering, especially in applied sciences like as applied chemistry and physics, computer sciences and automation, electronics and telecommunication. The main subject of the paper is to express fragmentation criteria in graph using a new method of investigation: terminal paths. Using terminal paths are defined most of the fragmentation criteria that are in use in molecular topology, but the fields of applications are more generally than that, as I mentioned before. Graphical examples of fragmentation are given for every fragmentation criteria. Note that all fragmentation is made with a computer program that implements a routine for every criterion.[1] A web routine for tracing all terminal paths in graph can be found at the address: http://vl.academicdirect.ro/molecular_topology/tpaths/ [1] M. V. Diudea, I. Gutman, L. Jäntschi, Molecular Topology, Nova Science, Commack, New York, 2001, 2002.

Introductory graph theory

CERN Document Server

Chartrand, Gary

1984-01-01

Graph theory is used today in the physical sciences, social sciences, computer science, and other areas. Introductory Graph Theory presents a nontechnical introduction to this exciting field in a clear, lively, and informative style. Author Gary Chartrand covers the important elementary topics of graph theory and its applications. In addition, he presents a large variety of proofs designed to strengthen mathematical techniques and offers challenging opportunities to have fun with mathematics. Ten major topics - profusely illustrated - include: Mathematical Models, Elementary Concepts of Grap

Growing hierarchical probabilistic self-organizing graphs.

Science.gov (United States)

López-Rubio, Ezequiel; Palomo, Esteban José

2011-07-01

Since the introduction of the growing hierarchical self-organizing map, much work has been done on self-organizing neural models with a dynamic structure. These models allow adjusting the layers of the model to the features of the input dataset. Here we propose a new self-organizing model which is based on a probabilistic mixture of multivariate Gaussian components. The learning rule is derived from the stochastic approximation framework, and a probabilistic criterion is used to control the growth of the model. Moreover, the model is able to adapt to the topology of each layer, so that a hierarchy of dynamic graphs is built. This overcomes the limitations of the self-organizing maps with a fixed topology, and gives rise to a faithful visualization method for high-dimensional data.

Creating more effective graphs

CERN Document Server

Robbins, Naomi B

2012-01-01

A succinct and highly readable guide to creating effective graphs The right graph can be a powerful tool for communicating information, improving a presentation, or conveying your point in print. If your professional endeavors call for you to present data graphically, here's a book that can help you do it more effectively. Creating More Effective Graphs gives you the basic knowledge and techniques required to choose and create appropriate graphs for a broad range of applications. Using real-world examples everyone can relate to, the author draws on her years of experience in gr

Graph Compression by BFS

Directory of Open Access Journals (Sweden)

Alberto Apostolico

2009-08-01

Full Text Available The Web Graph is a large-scale graph that does not fit in main memory, so that lossless compression methods have been proposed for it. This paper introduces a compression scheme that combines efficient storage with fast retrieval for the information in a node. The scheme exploits the properties of the Web Graph without assuming an ordering of the URLs, so that it may be applied to more general graphs. Tests on some datasets of use achieve space savings of about 10% over existing methods.

Experimental quantum annealing: case study involving the graph isomorphism problem.

Science.gov (United States)

Zick, Kenneth M; Shehab, Omar; French, Matthew

2015-06-08

Quantum annealing is a proposed combinatorial optimization technique meant to exploit quantum mechanical effects such as tunneling and entanglement. Real-world quantum annealing-based solvers require a combination of annealing and classical pre- and post-processing; at this early stage, little is known about how to partition and optimize the processing. This article presents an experimental case study of quantum annealing and some of the factors involved in real-world solvers, using a 504-qubit D-Wave Two machine and the graph isomorphism problem. To illustrate the role of classical pre-processing, a compact Hamiltonian is presented that enables a reduced Ising model for each problem instance. On random N-vertex graphs, the median number of variables is reduced from N(2) to fewer than N log2 N and solvable graph sizes increase from N = 5 to N = 13. Additionally, error correction via classical post-processing majority voting is evaluated. While the solution times are not competitive with classical approaches to graph isomorphism, the enhanced solver ultimately classified correctly every problem that was mapped to the processor and demonstrated clear advantages over the baseline approach. The results shed some light on the nature of real-world quantum annealing and the associated hybrid classical-quantum solvers.

Graphing Inequalities, Connecting Meaning

Science.gov (United States)

Switzer, J. Matt

2014-01-01

Students often have difficulty with graphing inequalities (see Filloy, Rojano, and Rubio 2002; Drijvers 2002), and J. Matt Switzer's students were no exception. Although students can produce graphs for simple inequalities, they often struggle when the format of the inequality is unfamiliar. Even when producing a correct graph of an…

Fuzzy Graph Language Recognizability

OpenAIRE

Kalampakas , Antonios; Spartalis , Stefanos; Iliadis , Lazaros

2012-01-01

Part 5: Fuzzy Logic; International audience; Fuzzy graph language recognizability is introduced along the lines of the established theory of syntactic graph language recognizability by virtue of the algebraic structure of magmoids. The main closure properties of the corresponding class are investigated and several interesting examples of fuzzy graph languages are examined.

Trace formulae and spectral statistics for discrete Laplacians on regular graphs (I)

Energy Technology Data Exchange (ETDEWEB)

Oren, Idan; Godel, Amit; Smilansky, Uzy [Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100 (Israel)], E-mail: idan.oren@weizmann.ac.il, E-mail: amit.godel@weizmann.ac.il, E-mail: uzy.smilansky@weizmann.ac.il

2009-10-16

Trace formulae for d-regular graphs are derived and used to express the spectral density in terms of the periodic walks on the graphs under consideration. The trace formulae depend on a parameter w which can be tuned continuously to assign different weights to different periodic orbit contributions. At the special value w = 1, the only periodic orbits which contribute are the non-back-scattering orbits, and the smooth part in the trace formula coincides with the Kesten-McKay expression. As w deviates from unity, non-vanishing weights are assigned to the periodic walks with backscatter, and the smooth part is modified in a consistent way. The trace formulae presented here are the tools to be used in the second paper in this sequence, for showing the connection between the spectral properties of d-regular graphs and the theory of random matrices.

Bell inequalities for graph states

International Nuclear Information System (INIS)

Toth, G.; Hyllus, P.; Briegel, H.J.; Guehne, O.

2005-01-01

Full text: In the last years graph states have attracted an increasing interest in the field of quantum information theory. Graph states form a family of multi-qubit states which comprises many popular states such as the GHZ states and the cluster states. They also play an important role in applications. For instance, measurement based quantum computation uses graph states as resources. From a theoretical point of view, it is remarkable that graph states allow for a simple description in terms of stabilizing operators. In this contribution, we investigate the non-local properties of graph states. We derive a family of Bell inequalities which require three measurement settings for each party and are maximally violated by graph states. In turn, any graph state violates at least one of the inequalities. We show that for certain types of graph states the violation of these inequalities increases exponentially with the number of qubits. We also discuss connections to other entanglement properties such as the positively of the partial transpose or the geometric measure of entanglement. (author)

Effects of Topological Randomness on Cooperation in a Deterministic Prisoner's Dilemma Game

International Nuclear Information System (INIS)

Zhang Mei; Yang Junzhong

2011-01-01

In this work, we consider an evolutionary prisoner's dilemma game on a homogeneous random network with the richest-following strategy adoption rule. By constructing homogeneous random networks from a regular ring graph, we investigate the effects of topological randomness on cooperation. In contrast to the ordinary view that the presence of small amount of shortcuts in ring graphs favors cooperation, we find the cooperation inhibition by weak topological randomness. The explanations on the observations are presented. (general)

Dynamic Representations of Sparse Graphs

DEFF Research Database (Denmark)

Brodal, Gerth Stølting; Fagerberg, Rolf

1999-01-01

We present a linear space data structure for maintaining graphs with bounded arboricity—a large class of sparse graphs containing e.g. planar graphs and graphs of bounded treewidth—under edge insertions, edge deletions, and adjacency queries. The data structure supports adjacency queries in worst...... case O(c) time, and edge insertions and edge deletions in amortized O(1) and O(c+log n) time, respectively, where n is the number of nodes in the graph, and c is the bound on the arboricity....

Multiple graph regularized protein domain ranking.

Science.gov (United States)

Wang, Jim Jing-Yan; Bensmail, Halima; Gao, Xin

2012-11-19

Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods. To tackle this problem, we have developed the Multiple Graph regularized Ranking algorithm, MultiG-Rank. Instead of using a single graph to regularize the ranking scores, MultiG-Rank approximates the intrinsic manifold of protein domain distribution by combining multiple initial graphs for the regularization. Graph weights are learned with ranking scores jointly and automatically, by alternately minimizing an objective function in an iterative algorithm. Experimental results on a subset of the ASTRAL SCOP protein domain database demonstrate that MultiG-Rank achieves a better ranking performance than single graph regularized ranking methods and pairwise similarity based ranking methods. The problem of graph model and parameter selection in graph regularized protein domain ranking can be solved effectively by combining multiple graphs. This aspect of generalization introduces a new frontier in applying multiple graphs to solving protein domain ranking applications.

Acyclicity in edge-colored graphs

DEFF Research Database (Denmark)

Gutin, Gregory; Jones, Mark; Sheng, Bin

2017-01-01

A walk W in edge-colored graphs is called properly colored (PC) if every pair of consecutive edges in W is of different color. We introduce and study five types of PC acyclicity in edge-colored graphs such that graphs of PC acyclicity of type i is a proper superset of graphs of acyclicity of type...

ON BIPOLAR SINGLE VALUED NEUTROSOPHIC GRAPHS

OpenAIRE

Said Broumi; Mohamed Talea; Assia Bakali; Florentin Smarandache

2016-01-01

In this article, we combine the concept of bipolar neutrosophic set and graph theory. We introduce the notions of bipolar single valued neutrosophic graphs, strong bipolar single valued neutrosophic graphs, complete bipolar single valued neutrosophic graphs, regular bipolar single valued neutrosophic graphs and investigate some of their related properties.

Practical graph mining with R

CERN Document Server

Hendrix, William; Jenkins, John; Padmanabhan, Kanchana; Chakraborty, Arpan

2014-01-01

Practical Graph Mining with R presents a "do-it-yourself" approach to extracting interesting patterns from graph data. It covers many basic and advanced techniques for the identification of anomalous or frequently recurring patterns in a graph, the discovery of groups or clusters of nodes that share common patterns of attributes and relationships, the extraction of patterns that distinguish one category of graphs from another, and the use of those patterns to predict the category of new graphs. Hands-On Application of Graph Data Mining Each chapter in the book focuses on a graph mining task, such as link analysis, cluster analysis, and classification. Through applications using real data sets, the book demonstrates how computational techniques can help solve real-world problems. The applications covered include network intrusion detection, tumor cell diagnostics, face recognition, predictive toxicology, mining metabolic and protein-protein interaction networks, and community detection in social networks. De...

A seminar on graph theory

CERN Document Server

Harary, Frank

2015-01-01

Presented in 1962-63 by experts at University College, London, these lectures offer a variety of perspectives on graph theory. Although the opening chapters form a coherent body of graph theoretic concepts, this volume is not a text on the subject but rather an introduction to the extensive literature of graph theory. The seminar's topics are geared toward advanced undergraduate students of mathematics.Lectures by this volume's editor, Frank Harary, include ""Some Theorems and Concepts of Graph Theory,"" ""Topological Concepts in Graph Theory,"" ""Graphical Reconstruction,"" and other introduc

Fuzzy Random Walkers with Second Order Bounds: An Asymmetric Analysis

Directory of Open Access Journals (Sweden)

Georgios Drakopoulos

2017-03-01

Full Text Available Edge-fuzzy graphs constitute an essential modeling paradigm across a broad spectrum of domains ranging from artificial intelligence to computational neuroscience and social network analysis. Under this model, fundamental graph properties such as edge length and graph diameter become stochastic and as such they are consequently expressed in probabilistic terms. Thus, algorithms for fuzzy graph analysis must rely on non-deterministic design principles. One such principle is Random Walker, which is based on a virtual entity and selects either edges or, like in this case, vertices of a fuzzy graph to visit. This allows the estimation of global graph properties through a long sequence of local decisions, making it a viable strategy candidate for graph processing software relying on native graph databases such as Neo4j. As a concrete example, Chebyshev Walktrap, a heuristic fuzzy community discovery algorithm relying on second order statistics and on the teleportation of the Random Walker, is proposed and its performance, expressed in terms of community coherence and number of vertex visits, is compared to the previously proposed algorithms of Markov Walktrap, Fuzzy Walktrap, and Fuzzy Newman–Girvan. In order to facilitate this comparison, a metric based on the asymmetric metrics of Tversky index and Kullback–Leibler divergence is used.

Object recognition in images via a factor graph model

Science.gov (United States)

He, Yong; Wang, Long; Wu, Zhaolin; Zhang, Haisu

2018-04-01

Object recognition in images suffered from huge search space and uncertain object profile. Recently, the Bag-of- Words methods are utilized to solve these problems, especially the 2-dimension CRF(Conditional Random Field) model. In this paper we suggest the method based on a general and flexible fact graph model, which can catch the long-range correlation in Bag-of-Words by constructing a network learning framework contrasted from lattice in CRF. Furthermore, we explore a parameter learning algorithm based on the gradient descent and Loopy Sum-Product algorithms for the factor graph model. Experimental results on Graz 02 dataset show that, the recognition performance of our method in precision and recall is better than a state-of-art method and the original CRF model, demonstrating the effectiveness of the proposed method.

Uniform Single Valued Neutrosophic Graphs

Directory of Open Access Journals (Sweden)

S. Broumi

2017-09-01

Full Text Available In this paper, we propose a new concept named the uniform single valued neutrosophic graph. An illustrative example and some properties are examined. Next, we develop an algorithmic approach for computing the complement of the single valued neutrosophic graph. A numerical example is demonstrated for computing the complement of single valued neutrosophic graphs and uniform single valued neutrosophic graph.

A nonlinear q-voter model with deadlocks on the Watts-Strogatz graph

Science.gov (United States)

Sznajd-Weron, Katarzyna; Michal Suszczynski, Karol

2014-07-01

We study the nonlinear $q$-voter model with deadlocks on a Watts-Strogats graph. Using Monte Carlo simulations, we obtain so called exit probability and exit time. We determine how network properties, such as randomness or density of links influence exit properties of a model.

Extremal graph theory

CERN Document Server

Bollobas, Bela

2004-01-01

The ever-expanding field of extremal graph theory encompasses a diverse array of problem-solving methods, including applications to economics, computer science, and optimization theory. This volume, based on a series of lectures delivered to graduate students at the University of Cambridge, presents a concise yet comprehensive treatment of extremal graph theory.Unlike most graph theory treatises, this text features complete proofs for almost all of its results. Further insights into theory are provided by the numerous exercises of varying degrees of difficulty that accompany each chapter. A

Multiple graph regularized protein domain ranking

KAUST Repository

Wang, Jim Jing-Yan

2012-11-19

Background: Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods.Results: To tackle this problem, we have developed the Multiple Graph regularized Ranking algorithm, MultiG-Rank. Instead of using a single graph to regularize the ranking scores, MultiG-Rank approximates the intrinsic manifold of protein domain distribution by combining multiple initial graphs for the regularization. Graph weights are learned with ranking scores jointly and automatically, by alternately minimizing an objective function in an iterative algorithm. Experimental results on a subset of the ASTRAL SCOP protein domain database demonstrate that MultiG-Rank achieves a better ranking performance than single graph regularized ranking methods and pairwise similarity based ranking methods.Conclusion: The problem of graph model and parameter selection in graph regularized protein domain ranking can be solved effectively by combining multiple graphs. This aspect of generalization introduces a new frontier in applying multiple graphs to solving protein domain ranking applications. 2012 Wang et al; licensee BioMed Central Ltd.

Multiple graph regularized protein domain ranking

KAUST Repository

Wang, Jim Jing-Yan; Bensmail, Halima; Gao, Xin

2012-01-01

Background: Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods.Results: To tackle this problem, we have developed the Multiple Graph regularized Ranking algorithm, MultiG-Rank. Instead of using a single graph to regularize the ranking scores, MultiG-Rank approximates the intrinsic manifold of protein domain distribution by combining multiple initial graphs for the regularization. Graph weights are learned with ranking scores jointly and automatically, by alternately minimizing an objective function in an iterative algorithm. Experimental results on a subset of the ASTRAL SCOP protein domain database demonstrate that MultiG-Rank achieves a better ranking performance than single graph regularized ranking methods and pairwise similarity based ranking methods.Conclusion: The problem of graph model and parameter selection in graph regularized protein domain ranking can be solved effectively by combining multiple graphs. This aspect of generalization introduces a new frontier in applying multiple graphs to solving protein domain ranking applications. 2012 Wang et al; licensee BioMed Central Ltd.

Multiple graph regularized protein domain ranking

Directory of Open Access Journals (Sweden)

Wang Jim

2012-11-01

Full Text Available Abstract Background Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods. Results To tackle this problem, we have developed the Multiple Graph regularized Ranking algorithm, MultiG-Rank. Instead of using a single graph to regularize the ranking scores, MultiG-Rank approximates the intrinsic manifold of protein domain distribution by combining multiple initial graphs for the regularization. Graph weights are learned with ranking scores jointly and automatically, by alternately minimizing an objective function in an iterative algorithm. Experimental results on a subset of the ASTRAL SCOP protein domain database demonstrate that MultiG-Rank achieves a better ranking performance than single graph regularized ranking methods and pairwise similarity based ranking methods. Conclusion The problem of graph model and parameter selection in graph regularized protein domain ranking can be solved effectively by combining multiple graphs. This aspect of generalization introduces a new frontier in applying multiple graphs to solving protein domain ranking applications.

Canonical Labelling of Site Graphs

Directory of Open Access Journals (Sweden)

Nicolas Oury

2013-06-01

Full Text Available We investigate algorithms for canonical labelling of site graphs, i.e. graphs in which edges bind vertices on sites with locally unique names. We first show that the problem of canonical labelling of site graphs reduces to the problem of canonical labelling of graphs with edge colourings. We then present two canonical labelling algorithms based on edge enumeration, and a third based on an extension of Hopcroft's partition refinement algorithm. All run in quadratic worst case time individually. However, one of the edge enumeration algorithms runs in sub-quadratic time for graphs with "many" automorphisms, and the partition refinement algorithm runs in sub-quadratic time for graphs with "few" bisimulation equivalences. This suite of algorithms was chosen based on the expectation that graphs fall in one of those two categories. If that is the case, a combined algorithm runs in sub-quadratic worst case time. Whether this expectation is reasonable remains an interesting open problem.

Random walk term weighting for information retrieval

DEFF Research Database (Denmark)

Blanco, R.; Lioma, Christina

2007-01-01

We present a way of estimating term weights for Information Retrieval (IR), using term co-occurrence as a measure of dependency between terms.We use the random walk graph-based ranking algorithm on a graph that encodes terms and co-occurrence dependencies in text, from which we derive term weights...

Random summing in a multi-detector counting system measuring mixtures of radionuclides of short and long half-lives

International Nuclear Information System (INIS)

Oxby, C.B.; Oldroyd, B.; Graham, S.G.

1979-01-01

A method is described for correcting a radiation spectrum for the distortion caused by random summing when a multidetector array is used to acquire events from a mixture of radionuclides whose half-lives may be long or short compared with the counting period. With our own counting system it was found that both the resolving time, and the fractions of the energy of a second signal which may be added to that of the immediately previous signal, i.e., the resolving time function, are dependent upon the energies of these two signals. The method requires knowledge of the losses which occur in a multidetector system e.g., live-time error and blocking losses, the variation of the resolving time function with signal energies, a standard spectrum of each radionuclide of the mixture and the fractions of them which constitute the mixture spectrum, the decay constant of each radionuclide, and the fraction of the total events recorded by the system being received by each detector. (orig.)

Domination criticality in product graphs

Directory of Open Access Journals (Sweden)

M.R. Chithra

2015-07-01

Full Text Available A connected dominating set is an important notion and has many applications in routing and management of networks. Graph products have turned out to be a good model of interconnection networks. This motivated us to study the Cartesian product of graphs G with connected domination number, γc(G=2,3 and characterize such graphs. Also, we characterize the k−γ-vertex (edge critical graphs and k−γc-vertex (edge critical graphs for k=2,3 where γ denotes the domination number of G. We also discuss the vertex criticality in grids.

Graph Creation, Visualisation and Transformation

Directory of Open Access Journals (Sweden)

Maribel Fernández

2010-03-01

Full Text Available We describe a tool to create, edit, visualise and compute with interaction nets - a form of graph rewriting systems. The editor, called GraphPaper, allows users to create and edit graphs and their transformation rules using an intuitive user interface. The editor uses the functionalities of the TULIP system, which gives us access to a wealth of visualisation algorithms. Interaction nets are not only a formalism for the specification of graphs, but also a rewrite-based computation model. We discuss graph rewriting strategies and a language to express them in order to perform strategic interaction net rewriting.

Graph Colouring Algorithms

DEFF Research Database (Denmark)

Husfeldt, Thore

2015-01-01

This chapter presents an introduction to graph colouring algorithms. The focus is on vertex-colouring algorithms that work for general classes of graphs with worst-case performance guarantees in a sequential model of computation. The presentation aims to demonstrate the breadth of available...

The fascinating world of graph theory

CERN Document Server

Benjamin, Arthur; Zhang, Ping

2015-01-01

Graph theory goes back several centuries and revolves around the study of graphs-mathematical structures showing relations between objects. With applications in biology, computer science, transportation science, and other areas, graph theory encompasses some of the most beautiful formulas in mathematics-and some of its most famous problems. The Fascinating World of Graph Theory explores the questions and puzzles that have been studied, and often solved, through graph theory. This book looks at graph theory's development and the vibrant individuals responsible for the field's growth. Introducin

Classical dynamics on graphs

International Nuclear Information System (INIS)

Barra, F.; Gaspard, P.

2001-01-01

We consider the classical evolution of a particle on a graph by using a time-continuous Frobenius-Perron operator that generalizes previous propositions. In this way, the relaxation rates as well as the chaotic properties can be defined for the time-continuous classical dynamics on graphs. These properties are given as the zeros of some periodic-orbit zeta functions. We consider in detail the case of infinite periodic graphs where the particle undergoes a diffusion process. The infinite spatial extension is taken into account by Fourier transforms that decompose the observables and probability densities into sectors corresponding to different values of the wave number. The hydrodynamic modes of diffusion are studied by an eigenvalue problem of a Frobenius-Perron operator corresponding to a given sector. The diffusion coefficient is obtained from the hydrodynamic modes of diffusion and has the Green-Kubo form. Moreover, we study finite but large open graphs that converge to the infinite periodic graph when their size goes to infinity. The lifetime of the particle on the open graph is shown to correspond to the lifetime of a system that undergoes a diffusion process before it escapes

Bayesian Analysis of two Censored Shifted Gompertz Mixture Distributions using Informative and Noninformative Priors

Directory of Open Access Journals (Sweden)

Tabassum Naz Sindhu

2017-03-01

Full Text Available This study deals with Bayesian analysis of shifted Gompertz mixture model under type-I censored samples assuming both informative and noninformative priors. We have discussed the Bayesian estimation of parameters of shifted Gompertz mixture model under the uniform, and gamma priors assuming three loss functions. Further, some properties of the model with some graphs of the mixture density are discussed. These properties include Bayes estimators, posterior risks and reliability function under simulation scheme. Bayes estimates are obtained considering two cases: (a when the shape parameter is known and (b when all parameters are unknown. We analyzed some simulated sets in order to investigate the effect of prior belief, loss functions, and performance of the proposed set of estimators of the mixture model parameters.

Quantum information processing with graph states

International Nuclear Information System (INIS)

Schlingemann, Dirk-Michael

2005-04-01

Graph states are multiparticle states which are associated with graphs. Each vertex of the graph corresponds to a single system or particle. The links describe quantum correlations (entanglement) between pairs of connected particles. Graph states were initiated independently by two research groups: On the one hand, graph states were introduced by Briegel and Raussendorf as a resource for a new model of one-way quantum computing, where algorithms are implemented by a sequence of measurements at single particles. On the other hand, graph states were developed by the author of this thesis and ReinhardWerner in Braunschweig, as a tool to build quantum error correcting codes, called graph codes. The connection between the two approaches was fully realized in close cooperation of both research groups. This habilitation thesis provides a survey of the theory of graph codes, focussing mainly, but not exclusively on the author's own research work. We present the theoretical and mathematical background for the analysis of graph codes. The concept of one-way quantum computing for general graph states is discussed. We explicitly show how to realize the encoding and decoding device of a graph code on a one-way quantum computer. This kind of implementation is to be seen as a mathematical description of a quantum memory device. In addition to that, we investigate interaction processes, which enable the creation of graph states on very large systems. Particular graph states can be created, for instance, by an Ising type interaction between next neighbor particles which sits at the points of an infinitely extended cubic lattice. Based on the theory of quantum cellular automata, we give a constructive characterization of general interactions which create a translationally invariant graph state. (orig.)

Fibonacci number of the tadpole graph

Directory of Open Access Journals (Sweden)

Joe DeMaio

2014-10-01

Full Text Available In 1982, Prodinger and Tichy defined the Fibonacci number of a graph G to be the number of independent sets of the graph G. They did so since the Fibonacci number of the path graph Pn is the Fibonacci number F(n+2 and the Fibonacci number of the cycle graph Cn is the Lucas number Ln. The tadpole graph Tn,k is the graph created by concatenating Cn and Pk with an edge from any vertex of Cn to a pendant of Pk for integers n=3 and k=0. This paper establishes formulae and identities for the Fibonacci number of the tadpole graph via algebraic and combinatorial methods.

On characterizing terrain visibility graphs

Directory of Open Access Journals (Sweden)

William Evans

2015-06-01

Full Text Available A terrain is an $x$-monotone polygonal line in the $xy$-plane. Two vertices of a terrain are mutually visible if and only if there is no terrain vertex on or above the open line segment connecting them. A graph whose vertices represent terrain vertices and whose edges represent mutually visible pairs of terrain vertices is called a terrain visibility graph. We would like to find properties that are both necessary and sufficient for a graph to be a terrain visibility graph; that is, we would like to characterize terrain visibility graphs.Abello et al. [Discrete and Computational Geometry, 14(3:331--358, 1995] showed that all terrain visibility graphs are “persistent”. They showed that the visibility information of a terrain point set implies some ordering requirements on the slopes of the lines connecting pairs of points in any realization, and as a step towards showing sufficiency, they proved that for any persistent graph $M$ there is a total order on the slopes of the (pseudo lines in a generalized configuration of points whose visibility graph is $M$.We give a much simpler proof of this result by establishing an orientation to every triple of vertices, reflecting some slope ordering requirements that are consistent with $M$ being the visibility graph, and prove that these requirements form a partial order. We give a faster algorithm to construct a total order on the slopes. Our approach attempts to clarify the implications of the graph theoretic properties on the ordering of the slopes, and may be interpreted as defining properties on an underlying oriented matroid that we show is a restricted type of $3$-signotope.

Network reconstruction via graph blending

Science.gov (United States)

Estrada, Rolando

2016-05-01

Graphs estimated from empirical data are often noisy and incomplete due to the difficulty of faithfully observing all the components (nodes and edges) of the true graph. This problem is particularly acute for large networks where the number of components may far exceed available surveillance capabilities. Errors in the observed graph can render subsequent analyses invalid, so it is vital to develop robust methods that can minimize these observational errors. Errors in the observed graph may include missing and spurious components, as well fused (multiple nodes are merged into one) and split (a single node is misinterpreted as many) nodes. Traditional graph reconstruction methods are only able to identify missing or spurious components (primarily edges, and to a lesser degree nodes), so we developed a novel graph blending framework that allows us to cast the full estimation problem as a simple edge addition/deletion problem. Armed with this framework, we systematically investigate the viability of various topological graph features, such as the degree distribution or the clustering coefficients, and existing graph reconstruction methods for tackling the full estimation problem. Our experimental results suggest that incorporating any topological feature as a source of information actually hinders reconstruction accuracy. We provide a theoretical analysis of this phenomenon and suggest several avenues for improving this estimation problem.

Interaction graphs

DEFF Research Database (Denmark)

Seiller, Thomas

2016-01-01

Interaction graphs were introduced as a general, uniform, construction of dynamic models of linear logic, encompassing all Geometry of Interaction (GoI) constructions introduced so far. This series of work was inspired from Girard's hyperfinite GoI, and develops a quantitative approach that should...... be understood as a dynamic version of weighted relational models. Until now, the interaction graphs framework has been shown to deal with exponentials for the constrained system ELL (Elementary Linear Logic) while keeping its quantitative aspect. Adapting older constructions by Girard, one can clearly define...... "full" exponentials, but at the cost of these quantitative features. We show here that allowing interpretations of proofs to use continuous (yet finite in a measure-theoretic sense) sets of states, as opposed to earlier Interaction Graphs constructions were these sets of states were discrete (and finite...

ℓ1/2-norm regularized nonnegative low-rank and sparse affinity graph for remote sensing image segmentation

Science.gov (United States)

Tian, Shu; Zhang, Ye; Yan, Yiming; Su, Nan

2016-10-01

Segmentation of real-world remote sensing images is a challenge due to the complex texture information with high heterogeneity. Thus, graph-based image segmentation methods have been attracting great attention in the field of remote sensing. However, most of the traditional graph-based approaches fail to capture the intrinsic structure of the feature space and are sensitive to noises. A ℓ-norm regularization-based graph segmentation method is proposed to segment remote sensing images. First, we use the occlusion of the random texture model (ORTM) to extract the local histogram features. Then, a ℓ-norm regularized low-rank and sparse representation (LNNLRS) is implemented to construct a ℓ-regularized nonnegative low-rank and sparse graph (LNNLRS-graph), by the union of feature subspaces. Moreover, the LNNLRS-graph has a high ability to discriminate the manifold intrinsic structure of highly homogeneous texture information. Meanwhile, the LNNLRS representation takes advantage of the low-rank and sparse characteristics to remove the noises and corrupted data. Last, we introduce the LNNLRS-graph into the graph regularization nonnegative matrix factorization to enhance the segmentation accuracy. The experimental results using remote sensing images show that when compared to five state-of-the-art image segmentation methods, the proposed method achieves more accurate segmentation results.

The Harary index of a graph

CERN Document Server

Xu, Kexiang; Trinajstić, Nenad

2015-01-01

This is the first book to focus on the topological index, the Harary index, of a graph, including its mathematical properties, chemical applications and some related and attractive open problems. This book is dedicated to Professor Frank Harary (1921—2005), the grandmaster of graph theory and its applications. It has be written by experts in the field of graph theory and its applications. For a connected graph G, as an important distance-based topological index, the Harary index H(G) is defined as the sum of the reciprocals of the distance between any two unordered vertices of the graph G. In this book, the authors report on the newest results on the Harary index of a graph. These results mainly concern external graphs with respect to the Harary index; the relations to other topological indices; its properties and applications to pure graph theory and chemical graph theory; and two significant variants, i.e., additively and multiplicatively weighted Harary indices. In the last chapter, we present a number o...

A Modal-Logic Based Graph Abstraction

NARCIS (Netherlands)

Bauer, J.; Boneva, I.B.; Kurban, M.E.; Rensink, Arend; Ehrig, H; Heckel, R.; Rozenberg, G.; Taentzer, G.

2008-01-01

Infinite or very large state spaces often prohibit the successful verification of graph transformation systems. Abstract graph transformation is an approach that tackles this problem by abstracting graphs to abstract graphs of bounded size and by lifting application of productions to abstract

Graph mining for next generation sequencing: leveraging the assembly graph for biological insights.

Science.gov (United States)

Warnke-Sommer, Julia; Ali, Hesham

2016-05-06

The assembly of Next Generation Sequencing (NGS) reads remains a challenging task. This is especially true for the assembly of metagenomics data that originate from environmental samples potentially containing hundreds to thousands of unique species. The principle objective of current assembly tools is to assemble NGS reads into contiguous stretches of sequence called contigs while maximizing for both accuracy and contig length. The end goal of this process is to produce longer contigs with the major focus being on assembly only. Sequence read assembly is an aggregative process, during which read overlap relationship information is lost as reads are merged into longer sequences or contigs. The assembly graph is information rich and capable of capturing the genomic architecture of an input read data set. We have developed a novel hybrid graph in which nodes represent sequence regions at different levels of granularity. This model, utilized in the assembly and analysis pipeline Focus, presents a concise yet feature rich view of a given input data set, allowing for the extraction of biologically relevant graph structures for graph mining purposes. Focus was used to create hybrid graphs to model metagenomics data sets obtained from the gut microbiomes of five individuals with Crohn's disease and eight healthy individuals. Repetitive and mobile genetic elements are found to be associated with hybrid graph structure. Using graph mining techniques, a comparative study of the Crohn's disease and healthy data sets was conducted with focus on antibiotics resistance genes associated with transposase genes. Results demonstrated significant differences in the phylogenetic distribution of categories of antibiotics resistance genes in the healthy and diseased patients. Focus was also evaluated as a pure assembly tool and produced excellent results when compared against the Meta-velvet, Omega, and UD-IDBA assemblers. Mining the hybrid graph can reveal biological phenomena captured

Distance-transitive graphs

NARCIS (Netherlands)

Cohen, A.M.; Beineke, L.W.; Wilson, R.J.; Cameron, P.J.

2004-01-01

In this chapter we investigate the classification of distance-transitive graphs: these are graphs whose automorphism groups are transitive on each of the sets of pairs of vertices at distance i, for i = 0, 1,.... We provide an introduction into the field. By use of the classification of finite

TrajGraph: A Graph-Based Visual Analytics Approach to Studying Urban Network Centralities Using Taxi Trajectory Data.

Science.gov (United States)

Huang, Xiaoke; Zhao, Ye; Yang, Jing; Zhang, Chong; Ma, Chao; Ye, Xinyue

2016-01-01

We propose TrajGraph, a new visual analytics method, for studying urban mobility patterns by integrating graph modeling and visual analysis with taxi trajectory data. A special graph is created to store and manifest real traffic information recorded by taxi trajectories over city streets. It conveys urban transportation dynamics which can be discovered by applying graph analysis algorithms. To support interactive, multiscale visual analytics, a graph partitioning algorithm is applied to create region-level graphs which have smaller size than the original street-level graph. Graph centralities, including Pagerank and betweenness, are computed to characterize the time-varying importance of different urban regions. The centralities are visualized by three coordinated views including a node-link graph view, a map view and a temporal information view. Users can interactively examine the importance of streets to discover and assess city traffic patterns. We have implemented a fully working prototype of this approach and evaluated it using massive taxi trajectories of Shenzhen, China. TrajGraph's capability in revealing the importance of city streets was evaluated by comparing the calculated centralities with the subjective evaluations from a group of drivers in Shenzhen. Feedback from a domain expert was collected. The effectiveness of the visual interface was evaluated through a formal user study. We also present several examples and a case study to demonstrate the usefulness of TrajGraph in urban transportation analysis.

Temporal Representation in Semantic Graphs

Energy Technology Data Exchange (ETDEWEB)

Levandoski, J J; Abdulla, G M

2007-08-07

A wide range of knowledge discovery and analysis applications, ranging from business to biological, make use of semantic graphs when modeling relationships and concepts. Most of the semantic graphs used in these applications are assumed to be static pieces of information, meaning temporal evolution of concepts and relationships are not taken into account. Guided by the need for more advanced semantic graph queries involving temporal concepts, this paper surveys the existing work involving temporal representations in semantic graphs.

The complexity of the matching-cut problem for planar graphs and other graph classes

NARCIS (Netherlands)

Bonsma, P.S.

2009-01-01

The Matching-Cut problem is the problem to decide whether a graph has an edge cut that is also a matching. Previously this problem was studied under the name of the Decomposable Graph Recognition problem, and proved to be -complete when restricted to graphs with maximum degree four. In this paper it

PRIVATE GRAPHS – ACCESS RIGHTS ON GRAPHS FOR SEAMLESS NAVIGATION

Directory of Open Access Journals (Sweden)

W. Dorner

2016-06-01

Full Text Available After the success of GNSS (Global Navigational Satellite Systems and navigation services for public streets, indoor seems to be the next big development in navigational services, relying on RTLS – Real Time Locating Services (e.g. WIFI and allowing seamless navigation. In contrast to navigation and routing services on public streets, seamless navigation will cause an additional challenge: how to make routing data accessible to defined users or restrict access rights for defined areas or only to parts of the graph to a defined user group? The paper will present case studies and data from literature, where seamless and especially indoor navigation solutions are presented (hospitals, industrial complexes, building sites, but the problem of restricted access rights was only touched from a real world, but not a technical perspective. The analysis of case studies will show, that the objective of navigation and the different target groups for navigation solutions will demand well defined access rights and require solutions, how to make only parts of a graph to a user or application available to solve a navigational task. The paper will therefore introduce the concept of private graphs, which is defined as a graph for navigational purposes covering the street, road or floor network of an area behind a public street and suggest different approaches how to make graph data for navigational purposes available considering access rights and data protection, privacy and security issues as well.

Integer Flows and Circuit Covers of Graphs and Signed Graphs

Science.gov (United States)

Cheng, Jian

The work in Chapter 2 is motivated by Tutte and Jaeger's pioneering work on converting modulo flows into integer-valued flows for ordinary graphs. For a signed graphs (G, sigma), we first prove that for each k ∈ {2, 3}, if (G, sigma) is (k - 1)-edge-connected and contains an even number of negative edges when k = 2, then every modulo k-flow of (G, sigma) can be converted into an integer-valued ( k + 1)-ow with a larger or the same support. We also prove that if (G, sigma) is odd-(2p+1)-edge-connected, then (G, sigma) admits a modulo circular (2 + 1/ p)-flows if and only if it admits an integer-valued circular (2 + 1/p)-flows, which improves all previous result by Xu and Zhang (DM2005), Schubert and Steffen (EJC2015), and Zhu (JCTB2015). Shortest circuit cover conjecture is one of the major open problems in graph theory. It states that every bridgeless graph G contains a set of circuits F such that each edge is contained in at least one member of F and the length of F is at most 7/5∥E(G)∥. This concept was recently generalized to signed graphs by Macajova et al. (JGT2015). In Chapter 3, we improve their upper bound from 11∥E( G)∥ to 14/3 ∥E(G)∥, and if G is 2-edgeconnected and has even negativeness, then it can be further reduced to 11/3 ∥E(G)∥. Tutte's 3-flow conjecture has been studied by many graph theorists in the last several decades. As a new approach to this conjecture, DeVos and Thomassen considered the vectors as ow values and found that there is a close relation between vector S1-flows and integer 3-NZFs. Motivated by their observation, in Chapter 4, we prove that if a graph G admits a vector S1-flow with rank at most two, then G admits an integer 3-NZF. The concept of even factors is highly related to the famous Four Color Theorem. We conclude this dissertation in Chapter 5 with an improvement of a recent result by Chen and Fan (JCTB2016) on the upperbound of even factors. We show that if a graph G contains an even factor, then it

Port-Hamiltonian Systems on Open Graphs

NARCIS (Netherlands)

Schaft, A.J. van der; Maschke, B.M.

2010-01-01

In this talk we discuss how to define in an intrinsic manner port-Hamiltonian dynamics on open graphs. Open graphs are graphs where some of the vertices are boundary vertices (terminals), which allow interconnection with other systems. We show that a directed graph carries two natural Dirac

Software for Graph Analysis and Visualization

Directory of Open Access Journals (Sweden)

M. I. Kolomeychenko

2014-01-01

Full Text Available This paper describes the software for graph storage, analysis and visualization. The article presents a comparative analysis of existing software for analysis and visualization of graphs, describes the overall architecture of application and basic principles of construction and operation of the main modules. Furthermore, a description of the developed graph storage oriented to storage and processing of large-scale graphs is presented. The developed algorithm for finding communities and implemented algorithms of autolayouts of graphs are the main functionality of the product. The main advantage of the developed software is high speed processing of large size networks (up to millions of nodes and links. Moreover, the proposed graph storage architecture is unique and has no analogues. The developed approaches and algorithms are optimized for operating with big graphs and have high productivity.

What Would a Graph Look Like in this Layout? A Machine Learning Approach to Large Graph Visualization.

Science.gov (United States)

Kwon, Oh-Hyun; Crnovrsanin, Tarik; Ma, Kwan-Liu

2018-01-01

Using different methods for laying out a graph can lead to very different visual appearances, with which the viewer perceives different information. Selecting a "good" layout method is thus important for visualizing a graph. The selection can be highly subjective and dependent on the given task. A common approach to selecting a good layout is to use aesthetic criteria and visual inspection. However, fully calculating various layouts and their associated aesthetic metrics is computationally expensive. In this paper, we present a machine learning approach to large graph visualization based on computing the topological similarity of graphs using graph kernels. For a given graph, our approach can show what the graph would look like in different layouts and estimate their corresponding aesthetic metrics. An important contribution of our work is the development of a new framework to design graph kernels. Our experimental study shows that our estimation calculation is considerably faster than computing the actual layouts and their aesthetic metrics. Also, our graph kernels outperform the state-of-the-art ones in both time and accuracy. In addition, we conducted a user study to demonstrate that the topological similarity computed with our graph kernel matches perceptual similarity assessed by human users.

Text-Filled Stacked Area Graphs

DEFF Research Database (Denmark)

Kraus, Martin

2011-01-01

-filled stacked area graphs; i.e., graphs that feature stacked areas that are filled with small-typed text. Since these graphs allow for computing the text layout automatically, it is possible to include large amounts of textual detail with very little effort. We discuss the most important challenges and some...... solutions for the design of text-filled stacked area graphs with the help of an exemplary visualization of the genres, publication years, and titles of a database of several thousand PC games....

On Graph Rewriting, Reduction and Evaluation

DEFF Research Database (Denmark)

Zerny, Ian

2010-01-01

We inter-derive two prototypical styles of graph reduction: reduction machines à la Turner and graph rewriting systems à la Barendregt et al. To this end, we adapt Danvy et al.'s mechanical program derivations from the world of terms to the world of graphs. We also outline how to inter-derive a t......We inter-derive two prototypical styles of graph reduction: reduction machines à la Turner and graph rewriting systems à la Barendregt et al. To this end, we adapt Danvy et al.'s mechanical program derivations from the world of terms to the world of graphs. We also outline how to inter...

Graph transformation tool contest 2008

NARCIS (Netherlands)

Rensink, Arend; van Gorp, Pieter

This special section is the outcome of the graph transformation tool contest organised during the Graph-Based Tools (GraBaTs) 2008 workshop, which took place as a satellite event of the International Conference on Graph Transformation (ICGT) 2008. The contest involved two parts: three “off-line case

On dominator colorings in graphs

Indian Academy of Sciences (India)

colors required for a dominator coloring of G is called the dominator .... Theorem 1.3 shows that the complete graph Kn is the only connected graph of order n ... Conversely, if a graph G satisfies condition (i) or (ii), it is easy to see that χd(G) =.

Graphs with branchwidth at most three

NARCIS (Netherlands)

Bodlaender, H.L.; Thilikos, D.M.

1997-01-01

In this paper we investigate both the structure of graphs with branchwidth at most three, as well as algorithms to recognise such graphs. We show that a graph has branchwidth at most three, if and only if it has treewidth at most three and does not contain the three-dimensional binary cube graph

Planar graphs theory and algorithms

CERN Document Server

Nishizeki, T

1988-01-01

Collected in this volume are most of the important theorems and algorithms currently known for planar graphs, together with constructive proofs for the theorems. Many of the algorithms are written in Pidgin PASCAL, and are the best-known ones; the complexities are linear or 0(nlogn). The first two chapters provide the foundations of graph theoretic notions and algorithmic techniques. The remaining chapters discuss the topics of planarity testing, embedding, drawing, vertex- or edge-coloring, maximum independence set, subgraph listing, planar separator theorem, Hamiltonian cycles, and single- or multicommodity flows. Suitable for a course on algorithms, graph theory, or planar graphs, the volume will also be useful for computer scientists and graph theorists at the research level. An extensive reference section is included.

Graph Quasicontinuous Functions and Densely Continuous Forms

Directory of Open Access Journals (Sweden)

Lubica Hola

2017-07-01

Full Text Available Let $X, Y$ be topological spaces. A function $f: X \\to Y$ is said to be graph quasicontinuous if there is a quasicontinuous function $g: X \\to Y$ with the graph of $g$ contained in the closure of the graph of $f$. There is a close relation between the notions of graph quasicontinuous functions and minimal usco maps as well as the notions of graph quasicontinuous functions and densely continuous forms. Every function with values in a compact Hausdorff space is graph quasicontinuous; more generally every locally compact function is graph quasicontinuous.

CORECLUSTER: A Degeneracy Based Graph Clustering Framework

OpenAIRE

Giatsidis , Christos; Malliaros , Fragkiskos; Thilikos , Dimitrios M. ,; Vazirgiannis , Michalis

2014-01-01

International audience; Graph clustering or community detection constitutes an important task forinvestigating the internal structure of graphs, with a plethora of applications in several domains. Traditional tools for graph clustering, such asspectral methods, typically suffer from high time and space complexity. In thisarticle, we present \\textsc{CoreCluster}, an efficient graph clusteringframework based on the concept of graph degeneracy, that can be used along withany known graph clusteri...

Tractable Algorithms for Proximity Search on Large Graphs

Science.gov (United States)

2010-07-01

Education never ends, Watson. It is a series of lessons with the greatest for the last. — Sir Arthur Conan Doyle’s Sherlock Holmes . 2.1 Introduction A...Doyle’s Sherlock Holmes . 5.1 Introduction In this thesis, our main goal is to design fast algorithms for proximity search in large graphs. In chapter 3...Conan Doyle’s Sherlock Holmes . In this thesis our main focus is on investigating some useful random walk based prox- imity measures. We have started

Coloring sums of extensions of certain graphs

Directory of Open Access Journals (Sweden)

Johan Kok

2017-12-01

Full Text Available We recall that the minimum number of colors that allow a proper coloring of graph $G$ is called the chromatic number of $G$ and denoted $\\chi(G$. Motivated by the introduction of the concept of the $b$-chromatic sum of a graph the concept of $\\chi'$-chromatic sum and $\\chi^+$-chromatic sum are introduced in this paper. The extended graph $G^x$ of a graph $G$ was recently introduced for certain regular graphs. This paper furthers the concepts of $\\chi'$-chromatic sum and $\\chi^+$-chromatic sum to extended paths and cycles. Bipartite graphs also receive some attention. The paper concludes with patterned structured graphs. These last said graphs are typically found in chemical and biological structures.

On a conjecture concerning helly circle graphs

Directory of Open Access Journals (Sweden)

Durán Guillermo

2003-01-01

Full Text Available We say that G is an e-circle graph if there is a bijection between its vertices and straight lines on the cartesian plane such that two vertices are adjacent in G if and only if the corresponding lines intersect inside the circle of radius one. This definition suggests a method for deciding whether a given graph G is an e-circle graph, by constructing a convenient system S of equations and inequations which represents the structure of G, in such a way that G is an e-circle graph if and only if S has a solution. In fact, e-circle graphs are exactly the circle graphs (intersection graphs of chords in a circle, and thus this method provides an analytic way for recognizing circle graphs. A graph G is a Helly circle graph if G is a circle graph and there exists a model of G by chords such that every three pairwise intersecting chords intersect at the same point. A conjecture by Durán (2000 states that G is a Helly circle graph if and only if G is a circle graph and contains no induced diamonds (a diamond is a graph formed by four vertices and five edges. Many unsuccessful efforts - mainly based on combinatorial and geometrical approaches - have been done in order to validate this conjecture. In this work, we utilize the ideas behind the definition of e-circle graphs and restate this conjecture in terms of an equivalence between two systems of equations and inequations, providing a new, analytic tool to deal with it.

Information Retrieval and Graph Analysis Approaches for Book Recommendation

OpenAIRE

Chahinez Benkoussas; Patrice Bellot

2015-01-01

A combination of multiple information retrieval approaches is proposed for the purpose of book recommendation. In this paper, book recommendation is based on complex user's query. We used different theoretical retrieval models: probabilistic as InL2 (Divergence from Randomness model) and language model and tested their interpolated combination. Graph analysis algorithms such as PageRank have been successful in Web environments. We consider the application of this algorithm in a new retrieval ...

Optimization Problems on Threshold Graphs

Directory of Open Access Journals (Sweden)

Elena Nechita

2010-06-01

Full Text Available During the last three decades, different types of decompositions have been processed in the field of graph theory. Among these we mention: decompositions based on the additivity of some characteristics of the graph, decompositions where the adjacency law between the subsets of the partition is known, decompositions where the subgraph induced by every subset of the partition must have predeterminate properties, as well as combinations of such decompositions. In this paper we characterize threshold graphs using the weakly decomposition, determine: density and stability number, Wiener index and Wiener polynomial for threshold graphs.

A Random Walk Approach to Query Informative Constraints for Clustering.

Science.gov (United States)

Abin, Ahmad Ali

2017-08-09

This paper presents a random walk approach to the problem of querying informative constraints for clustering. The proposed method is based on the properties of the commute time, that is the expected time taken for a random walk to travel between two nodes and return, on the adjacency graph of data. Commute time has the nice property of that, the more short paths connect two given nodes in a graph, the more similar those nodes are. Since computing the commute time takes the Laplacian eigenspectrum into account, we use this property in a recursive fashion to query informative constraints for clustering. At each recursion, the proposed method constructs the adjacency graph of data and utilizes the spectral properties of the commute time matrix to bipartition the adjacency graph. Thereafter, the proposed method benefits from the commute times distance on graph to query informative constraints between partitions. This process iterates for each partition until the stop condition becomes true. Experiments on real-world data show the efficiency of the proposed method for constraints selection.

Hierarchy of modular graph identities

Energy Technology Data Exchange (ETDEWEB)

D’Hoker, Eric; Kaidi, Justin [Mani L. Bhaumik Institute for Theoretical Physics, Department of Physics and Astronomy,University of California,Los Angeles, CA 90095 (United States)

2016-11-09

The low energy expansion of Type II superstring amplitudes at genus one is organized in terms of modular graph functions associated with Feynman graphs of a conformal scalar field on the torus. In earlier work, surprising identities between two-loop graphs at all weights, and between higher-loop graphs of weights four and five were constructed. In the present paper, these results are generalized in two complementary directions. First, all identities at weight six and all dihedral identities at weight seven are obtained and proven. Whenever the Laurent polynomial at the cusp is available, the form of these identities confirms the pattern by which the vanishing of the Laurent polynomial governs the full modular identity. Second, the family of modular graph functions is extended to include all graphs with derivative couplings and worldsheet fermions. These extended families of modular graph functions are shown to obey a hierarchy of inhomogeneous Laplace eigenvalue equations. The eigenvalues are calculated analytically for the simplest infinite sub-families and obtained by Maple for successively more complicated sub-families. The spectrum is shown to consist solely of eigenvalues s(s−1) for positive integers s bounded by the weight, with multiplicities which exhibit rich representation-theoretic patterns.

Hierarchy of modular graph identities

International Nuclear Information System (INIS)

D’Hoker, Eric; Kaidi, Justin

2016-01-01

The low energy expansion of Type II superstring amplitudes at genus one is organized in terms of modular graph functions associated with Feynman graphs of a conformal scalar field on the torus. In earlier work, surprising identities between two-loop graphs at all weights, and between higher-loop graphs of weights four and five were constructed. In the present paper, these results are generalized in two complementary directions. First, all identities at weight six and all dihedral identities at weight seven are obtained and proven. Whenever the Laurent polynomial at the cusp is available, the form of these identities confirms the pattern by which the vanishing of the Laurent polynomial governs the full modular identity. Second, the family of modular graph functions is extended to include all graphs with derivative couplings and worldsheet fermions. These extended families of modular graph functions are shown to obey a hierarchy of inhomogeneous Laplace eigenvalue equations. The eigenvalues are calculated analytically for the simplest infinite sub-families and obtained by Maple for successively more complicated sub-families. The spectrum is shown to consist solely of eigenvalues s(s−1) for positive integers s bounded by the weight, with multiplicities which exhibit rich representation-theoretic patterns.

Well-covered graphs and factors

DEFF Research Database (Denmark)

Randerath, Bert; Vestergaard, Preben D.

2006-01-01

A maximum independent set of vertices in a graph is a set of pairwise nonadjacent vertices of largest cardinality α. Plummer defined a graph to be well-covered, if every independent set is contained in a maximum independent set of G. Every well-covered graph G without isolated vertices has a perf...

On the centrality of some graphs

Directory of Open Access Journals (Sweden)

Vecdi Aytac

2017-10-01

Full Text Available A central issue in the analysis of complex networks is the assessment of their stability and vulnerability. A variety of measures have been proposed in the literature to quantify the stability of networks and a number of graph-theoretic parameters have been used to derive formulas for calculating network reliability. Different measures for graph vulnerability have been introduced so far to study different aspects of the graph behavior after removal of vertices or links such as connectivity, toughness, scattering number, binding number, residual closeness and integrity. In this paper, we consider betweenness centrality of a graph. Betweenness centrality of a vertex of a graph is portion of the shortest paths all pairs of vertices passing through a given vertex. In this paper, we obtain exact values for betweenness centrality for some wheel related graphs namely gear, helm, sunflower and friendship graphs.

Enabling Graph Appliance for Genome Assembly

Energy Technology Data Exchange (ETDEWEB)

Singh, Rina [ORNL; Graves, Jeffrey A [ORNL; Lee, Sangkeun (Matt) [ORNL; Sukumar, Sreenivas R [ORNL; Shankar, Mallikarjun [ORNL

2015-01-01

In recent years, there has been a huge growth in the amount of genomic data available as reads generated from various genome sequencers. The number of reads generated can be huge, ranging from hundreds to billions of nucleotide, each varying in size. Assembling such large amounts of data is one of the challenging computational problems for both biomedical and data scientists. Most of the genome assemblers developed have used de Bruijn graph techniques. A de Bruijn graph represents a collection of read sequences by billions of vertices and edges, which require large amounts of memory and computational power to store and process. This is the major drawback to de Bruijn graph assembly. Massively parallel, multi-threaded, shared memory systems can be leveraged to overcome some of these issues. The objective of our research is to investigate the feasibility and scalability issues of de Bruijn graph assembly on Cray s Urika-GD system; Urika-GD is a high performance graph appliance with a large shared memory and massively multithreaded custom processor designed for executing SPARQL queries over large-scale RDF data sets. However, to the best of our knowledge, there is no research on representing a de Bruijn graph as an RDF graph or finding Eulerian paths in RDF graphs using SPARQL for potential genome discovery. In this paper, we address the issues involved in representing a de Bruin graphs as RDF graphs and propose an iterative querying approach for finding Eulerian paths in large RDF graphs. We evaluate the performance of our implementation on real world ebola genome datasets and illustrate how genome assembly can be accomplished with Urika-GD using iterative SPARQL queries.

On 4-critical t-perfect graphs

OpenAIRE

Benchetrit, Yohann

2016-01-01

It is an open question whether the chromatic number of $t$-perfect graphs is bounded by a constant. The largest known value for this parameter is 4, and the only example of a 4-critical $t$-perfect graph, due to Laurent and Seymour, is the complement of the line graph of the prism $\\Pi$ (a graph is 4-critical if it has chromatic number 4 and all its proper induced subgraphs are 3-colorable). In this paper, we show a new example of a 4-critical $t$-perfect graph: the complement of the line gra...

Local adjacency metric dimension of sun graph and stacked book graph

Science.gov (United States)

Yulisda Badri, Alifiah; Darmaji

2018-03-01

A graph is a mathematical system consisting of a non-empty set of nodes and a set of empty sides. One of the topics to be studied in graph theory is the metric dimension. Application in the metric dimension is the navigation robot system on a path. Robot moves from one vertex to another vertex in the field by minimizing the errors that occur in translating the instructions (code) obtained from the vertices of that location. To move the robot must give different instructions (code). In order for the robot to move efficiently, the robot must be fast to translate the code of the nodes of the location it passes. so that the location vertex has a minimum distance. However, if the robot must move with the vertex location on a very large field, so the robot can not detect because the distance is too far.[6] In this case, the robot can determine its position by utilizing location vertices based on adjacency. The problem is to find the minimum cardinality of the required location vertex, and where to put, so that the robot can determine its location. The solution to this problem is the dimension of adjacency metric and adjacency metric bases. Rodrguez-Velzquez and Fernau combine the adjacency metric dimensions with local metric dimensions, thus becoming the local adjacency metric dimension. In the local adjacency metric dimension each vertex in the graph may have the same adjacency representation as the terms of the vertices. To obtain the local metric dimension of values in the graph of the Sun and the stacked book graph is used the construction method by considering the representation of each adjacent vertex of the graph.

Mechatronic modeling and simulation using bond graphs

CERN Document Server

Das, Shuvra

2009-01-01

Introduction to Mechatronics and System ModelingWhat Is Mechatronics?What Is a System and Why Model Systems?Mathematical Modeling Techniques Used in PracticeSoftwareBond Graphs: What Are They?Engineering SystemsPortsGeneralized VariablesBond GraphsBasic Components in SystemsA Brief Note about Bond Graph Power DirectionsSummary of Bond Direction RulesDrawing Bond Graphs for Simple Systems: Electrical and MechanicalSimplification Rules for Junction StructureDrawing Bond Graphs for Electrical SystemsDrawing Bond Graphs for Mechanical SystemsCausalityDrawing Bond Graphs for Hydraulic and Electronic Components and SystemsSome Basic Properties and Concepts for FluidsBond Graph Model of Hydraulic SystemsElectronic SystemsDeriving System Equations from Bond GraphsSystem VariablesDeriving System EquationsTackling Differential CausalityAlgebraic LoopsSolution of Model Equations and Their InterpretationZeroth Order SystemsFirst Order SystemsSecond Order SystemTransfer Functions and Frequency ResponsesNumerical Solution ...

Expert interpretation of bar and line graphs: The role of graphicacy in reducing the effect of graph format.

Directory of Open Access Journals (Sweden)

David ePeebles

2015-10-01

Full Text Available The distinction between informational and computational equivalence of representations, first articulated by Larkin and Simon (1987 has been a fundamental principle in the analysis of diagrammatic reasoning which has been supported empirically on numerous occasions. We present an experiment that investigates this principle in relation to the performance of expert graph users of 2 x 2 'interaction' bar and line graphs. The study sought to determine whether expert interpretation is affected by graph format in the same way that novice interpretations are. The findings revealed that, unlike novices - and contrary to the assumptions of several graph comprehension models - experts' performance was the same for both graph formats, with their interpretation of bar graphs being no worse than that for line graphs. We discuss the implications of the study for guidelines for presenting such data and for models of expert graph comprehension.

Proving termination of graph transformation systems using weighted type graphs over semirings

NARCIS (Netherlands)

Bruggink, H.J.S.; König, B.; Nolte, D.; Zantema, H.; Parisi-Presicce, F.; Westfechtel, B.

2015-01-01

We introduce techniques for proving uniform termination of graph transformation systems, based on matrix interpretations for string rewriting. We generalize this technique by adapting it to graph rewriting instead of string rewriting and by generalizing to ordered semirings. In this way we obtain a

Theoretical issues in quantum computing: Graph isomorphism, PageRank, and Hamiltonian determination

Science.gov (United States)

Rudinger, Kenneth Michael

This thesis explores several theoretical questions pertaining to quantum computing. First we examine several questions regarding multi-particle quantum random walk-based algorithms for the graph isomorphism problem. We find that there exists a non-trivial difference between continuous-time walks of one and two non-interacting particles as compared to non-interacting walks of three or more particles, in that the latter are able to distinguish many strongly regular graphs (SRGs), a class of graphs with many graph pairs that are difficult to distinguish. We demonstrate analytically where this distinguishing power comes from, and we show numerically that three-particle and four-particle non-interacting continuous-time walks can distinguish many pairs of strongly regular graphs. We additionally show that this distinguishing power, while it grows with particle number, is bounded, so that no continuous-time non-interacting walk of fixed particle number can distinguish all strongly regular graphs. We then investigate the relationship between continuous-time and discrete-time walks, in the context of the graph isomorphism problem. While it has been previously demonstrated numerically that discrete-time walks of non-interacting particles can distinguish some SRGs, we demonstrate where this distinguishing power comes from. We also show that while no continuous-time non-interacting walk of fixed particle number can distinguish SRGs, it remains a possibility that such a discrete-time walk could, leaving open the possibility of a non-trivial difference between discrete-time and continuous-time walks. The last piece of our work on graph isomorphism examines limitations on certain kinds of continuous-time walk-based algorithms for distinguishing graphs. We show that a very general class of continuous-time walk algorithms, with a broad class of allowable interactions, cannot distinguish all graphs. We next consider a previously-proposed quantum adiabatic algorithm for computing the

Application de la théorie des graphes au traitement de la carte géologique Applying the Theory of Graphs to the Treatment of Geological Maps

Directory of Open Access Journals (Sweden)

Bouillé F.

2006-11-01

Full Text Available La saisie des informations d'une carte géologique par les méthodes classiques (grilles ou relevés aléatoires de courbes ne constitue pas une base de données opérationnelle. Par contre, l'assimilation des limites géologiques à un graphe orienté répond aux critères d'optimalité (encombrement très réduit, temps minimal, fiabilité, et permet une digitalisation rationnelle de la carte, une bonne structuration du fichier, et la réalisation d'applications intéressantes : restitutions graphiques sélectives à toutes échelles, calculs de pendages, surfaces, volumes, études de corrélation. Nous avons donc établi une chaîne de traitement de la carte géologique dont chaque maillon (saisie des informations; contrôle, mise à jour, consultation, application opère sur un ou plusieurs graphes. Obtaining data from geological maps by conventional methods (grids or random curve plotting is not an operational data base. However, the comparison of geological boundaries with a directional graph meets criteria of optimalness (very small bulk, minimum time, reliability and makes it possible to digitize the map rationally, to structure the file properly and to achieve significant applications such as selective graph plotting on all scales, calculating dips, areas and volumes, and making correlotion analyses. Therefore, we worked out a geological map processing sequence in which each element (data acquisition, checking, updating, consulting, applications operates on one or several graphs.

DIMENSI METRIK GRAPH LOBSTER Ln (q;r

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PANDE GDE DONY GUMILAR

2013-05-01

Full Text Available The metric dimension of connected graph G is the cardinality of minimum resolving set in graph G. In this research, we study how to find the metric dimension of lobster graph Ln (q;r. Lobster graph Ln (q;r is a regular lobster graph with vertices backbone on the main path, every backbone vertex is connected to q hand vertices and every hand vertex is connected to r finger vertices, with n, q, r element of N. We obtain the metric dimension of lobster graph L2 (1;1 is 1, the metric dimension of lobster graph L2 (1;1 for n > 2 is 2.

Summary: beyond fault trees to fault graphs

International Nuclear Information System (INIS)

Alesso, H.P.; Prassinos, P.; Smith, C.F.

1984-09-01

Fault Graphs are the natural evolutionary step over a traditional fault-tree model. A Fault Graph is a failure-oriented directed graph with logic connectives that allows cycles. We intentionally construct the Fault Graph to trace the piping and instrumentation drawing (P and ID) of the system, but with logical AND and OR conditions added. Then we evaluate the Fault Graph with computer codes based on graph-theoretic methods. Fault Graph computer codes are based on graph concepts, such as path set (a set of nodes traveled on a path from one node to another) and reachability (the complete set of all possible paths between any two nodes). These codes are used to find the cut-sets (any minimal set of component failures that will fail the system) and to evaluate the system reliability

Interactive Graph Layout of a Million Nodes

Directory of Open Access Journals (Sweden)

Peng Mi

2016-12-01

Full Text Available Sensemaking of large graphs, specifically those with millions of nodes, is a crucial task in many fields. Automatic graph layout algorithms, augmented with real-time human-in-the-loop interaction, can potentially support sensemaking of large graphs. However, designing interactive algorithms to achieve this is challenging. In this paper, we tackle the scalability problem of interactive layout of large graphs, and contribute a new GPU-based force-directed layout algorithm that exploits graph topology. This algorithm can interactively layout graphs with millions of nodes, and support real-time interaction to explore alternative graph layouts. Users can directly manipulate the layout of vertices in a force-directed fashion. The complexity of traditional repulsive force computation is reduced by approximating calculations based on the hierarchical structure of multi-level clustered graphs. We evaluate the algorithm performance, and demonstrate human-in-the-loop layout in two sensemaking case studies. Moreover, we summarize lessons learned for designing interactive large graph layout algorithms on the GPU.

Eulerian Graphs and Related Topics

CERN Document Server

Fleischner, Herbert

1990-01-01

The two volumes comprising Part 1 of this work embrace the theme of Eulerian trails and covering walks. They should appeal both to researchers and students, as they contain enough material for an undergraduate or graduate graph theory course which emphasizes Eulerian graphs, and thus can be read by any mathematician not yet familiar with graph theory. But they are also of interest to researchers in graph theory because they contain many recent results, some of which are only partial solutions to more general problems. A number of conjectures have been included as well. Various problems (such a

The One Universal Graph — a free and open graph database

Science.gov (United States)

Ng, Liang S.; Champion, Corbin

2016-02-01

Recent developments in graph database mostly are huge projects involving big organizations, big operations and big capital, as the name Big Data attests. We proposed the concept of One Universal Graph (OUG) which states that all observable and known objects and concepts (physical, conceptual or digitally represented) can be connected with only one single graph; furthermore the OUG can be implemented with a very simple text file format with free software, capable of being executed on Android or smaller devices. As such the One Universal Graph Data Exchange (GOUDEX) modules can potentially be installed on hundreds of millions of Android devices and Intel compatible computers shipped annually. Coupled with its open nature and ability to connect to existing leading search engines and databases currently in operation, GOUDEX has the potential to become the largest and a better interface for users and programmers to interact with the data on the Internet. With a Web User Interface for users to use and program in native Linux environment, Free Crowdware implemented in GOUDEX can help inexperienced users learn programming with better organized documentation for free software, and is able to manage programmer's contribution down to a single line of code or a single variable in software projects. It can become the first practically realizable “Internet brain” on which a global artificial intelligence system can be implemented. Being practically free and open, One Universal Graph can have significant applications in robotics, artificial intelligence as well as social networks.

Degree-based graph construction

International Nuclear Information System (INIS)

Kim, Hyunju; Toroczkai, Zoltan; Erdos, Peter L; Miklos, Istvan; Szekely, Laszlo A

2009-01-01

Degree-based graph construction is a ubiquitous problem in network modelling (Newman et al 2006 The Structure and Dynamics of Networks (Princeton Studies in Complexity) (Princeton, NJ: Princeton University Press), Boccaletti et al 2006 Phys. Rep. 424 175), ranging from social sciences to chemical compounds and biochemical reaction networks in the cell. This problem includes existence, enumeration, exhaustive construction and sampling questions with aspects that are still open today. Here we give necessary and sufficient conditions for a sequence of nonnegative integers to be realized as a simple graph's degree sequence, such that a given (but otherwise arbitrary) set of connections from an arbitrarily given node is avoided. We then use this result to present a swap-free algorithm that builds all simple graphs realizing a given degree sequence. In a wider context, we show that our result provides a greedy construction method to build all the f-factor subgraphs (Tutte 1952 Can. J. Math. 4 314) embedded within K n setmn S k , where K n is the complete graph and S k is a star graph centred on one of the nodes. (fast track communication)

Downhill Domination in Graphs

Directory of Open Access Journals (Sweden)

Haynes Teresa W.

2014-08-01

Full Text Available A path π = (v1, v2, . . . , vk+1 in a graph G = (V,E is a downhill path if for every i, 1 ≤ i ≤ k, deg(vi ≥ deg(vi+1, where deg(vi denotes the degree of vertex vi ∈ V. The downhill domination number equals the minimum cardinality of a set S ⊆ V having the property that every vertex v ∈ V lies on a downhill path originating from some vertex in S. We investigate downhill domination numbers of graphs and give upper bounds. In particular, we show that the downhill domination number of a graph is at most half its order, and that the downhill domination number of a tree is at most one third its order. We characterize the graphs obtaining each of these bounds

Proving relations between modular graph functions

International Nuclear Information System (INIS)

Basu, Anirban

2016-01-01

We consider modular graph functions that arise in the low energy expansion of the four graviton amplitude in type II string theory. The vertices of these graphs are the positions of insertions of vertex operators on the toroidal worldsheet, while the links are the scalar Green functions connecting the vertices. Graphs with four and five links satisfy several non-trivial relations, which have been proved recently. We prove these relations by using elementary properties of Green functions and the details of the graphs. We also prove a relation between modular graph functions with six links. (paper)

Semantic graphs and associative memories

Science.gov (United States)

Pomi, Andrés; Mizraji, Eduardo

2004-12-01

Graphs have been increasingly utilized in the characterization of complex networks from diverse origins, including different kinds of semantic networks. Human memories are associative and are known to support complex semantic nets; these nets are represented by graphs. However, it is not known how the brain can sustain these semantic graphs. The vision of cognitive brain activities, shown by modern functional imaging techniques, assigns renewed value to classical distributed associative memory models. Here we show that these neural network models, also known as correlation matrix memories, naturally support a graph representation of the stored semantic structure. We demonstrate that the adjacency matrix of this graph of associations is just the memory coded with the standard basis of the concept vector space, and that the spectrum of the graph is a code invariant of the memory. As long as the assumptions of the model remain valid this result provides a practical method to predict and modify the evolution of the cognitive dynamics. Also, it could provide us with a way to comprehend how individual brains that map the external reality, almost surely with different particular vector representations, are nevertheless able to communicate and share a common knowledge of the world. We finish presenting adaptive association graphs, an extension of the model that makes use of the tensor product, which provides a solution to the known problem of branching in semantic nets.

RNA graph partitioning for the discovery of RNA modularity: a novel application of graph partition algorithm to biology.

Directory of Open Access Journals (Sweden)

Namhee Kim

Full Text Available Graph representations have been widely used to analyze and design various economic, social, military, political, and biological networks. In systems biology, networks of cells and organs are useful for understanding disease and medical treatments and, in structural biology, structures of molecules can be described, including RNA structures. In our RNA-As-Graphs (RAG framework, we represent RNA structures as tree graphs by translating unpaired regions into vertices and helices into edges. Here we explore the modularity of RNA structures by applying graph partitioning known in graph theory to divide an RNA graph into subgraphs. To our knowledge, this is the first application of graph partitioning to biology, and the results suggest a systematic approach for modular design in general. The graph partitioning algorithms utilize mathematical properties of the Laplacian eigenvector (µ2 corresponding to the second eigenvalues (λ2 associated with the topology matrix defining the graph: λ2 describes the overall topology, and the sum of µ2's components is zero. The three types of algorithms, termed median, sign, and gap cuts, divide a graph by determining nodes of cut by median, zero, and largest gap of µ2's components, respectively. We apply these algorithms to 45 graphs corresponding to all solved RNA structures up through 11 vertices (∼ 220 nucleotides. While we observe that the median cut divides a graph into two similar-sized subgraphs, the sign and gap cuts partition a graph into two topologically-distinct subgraphs. We find that the gap cut produces the best biologically-relevant partitioning for RNA because it divides RNAs at less stable connections while maintaining junctions intact. The iterative gap cuts suggest basic modules and assembly protocols to design large RNA structures. Our graph substructuring thus suggests a systematic approach to explore the modularity of biological networks. In our applications to RNA structures, subgraphs

A generalization of total graphs

Indian Academy of Sciences (India)

M Afkhami

2018-04-12

Apr 12, 2018 ... product of any lower triangular matrix with the transpose of any element of U belongs to U. The ... total graph of R, which is denoted by T( (R)), is a simple graph with all elements of R as vertices, and ...... [9] Badawi A, On dot-product graph of a commutative ring, Communications in Algebra 43 (2015). 43–50.

Optimal Quantum Spatial Search on Random Temporal Networks

Science.gov (United States)

Chakraborty, Shantanav; Novo, Leonardo; Di Giorgio, Serena; Omar, Yasser

2017-12-01

To investigate the performance of quantum information tasks on networks whose topology changes in time, we study the spatial search algorithm by continuous time quantum walk to find a marked node on a random temporal network. We consider a network of n nodes constituted by a time-ordered sequence of Erdös-Rényi random graphs G (n ,p ), where p is the probability that any two given nodes are connected: After every time interval τ , a new graph G (n ,p ) replaces the previous one. We prove analytically that, for any given p , there is always a range of values of τ for which the running time of the algorithm is optimal, i.e., O (√{n }), even when search on the individual static graphs constituting the temporal network is suboptimal. On the other hand, there are regimes of τ where the algorithm is suboptimal even when each of the underlying static graphs are sufficiently connected to perform optimal search on them. From this first study of quantum spatial search on a time-dependent network, it emerges that the nontrivial interplay between temporality and connectivity is key to the algorithmic performance. Moreover, our work can be extended to establish high-fidelity qubit transfer between any two nodes of the network. Overall, our findings show that one can exploit temporality to achieve optimal quantum information tasks on dynamical random networks.

Optimal Quantum Spatial Search on Random Temporal Networks.

Science.gov (United States)

Chakraborty, Shantanav; Novo, Leonardo; Di Giorgio, Serena; Omar, Yasser

2017-12-01

To investigate the performance of quantum information tasks on networks whose topology changes in time, we study the spatial search algorithm by continuous time quantum walk to find a marked node on a random temporal network. We consider a network of n nodes constituted by a time-ordered sequence of Erdös-Rényi random graphs G(n,p), where p is the probability that any two given nodes are connected: After every time interval τ, a new graph G(n,p) replaces the previous one. We prove analytically that, for any given p, there is always a range of values of τ for which the running time of the algorithm is optimal, i.e., O(sqrt[n]), even when search on the individual static graphs constituting the temporal network is suboptimal. On the other hand, there are regimes of τ where the algorithm is suboptimal even when each of the underlying static graphs are sufficiently connected to perform optimal search on them. From this first study of quantum spatial search on a time-dependent network, it emerges that the nontrivial interplay between temporality and connectivity is key to the algorithmic performance. Moreover, our work can be extended to establish high-fidelity qubit transfer between any two nodes of the network. Overall, our findings show that one can exploit temporality to achieve optimal quantum information tasks on dynamical random networks.

Decomposing a planar graph into an independent set and a 3-degenerate graph

DEFF Research Database (Denmark)

Thomassen, Carsten

2001-01-01

We prove the conjecture made by O. V. Borodin in 1976 that the vertex set of every planar graph can be decomposed into an independent set and a set inducing a 3-degenerate graph. (C) 2001 Academic Press....

Commuting graphs of matrix algebras

International Nuclear Information System (INIS)

Akbari, S.; Bidkhori, H.; Mohammadian, A.

2006-08-01

The commuting graph of a ring R, denoted by Γ(R), is a graph whose vertices are all non- central elements of R and two distinct vertices x and y are adjacent if and only if xy = yx. The commuting graph of a group G, denoted by Γ(G), is similarly defined. In this paper we investigate some graph theoretic properties of Γ(M n (F)), where F is a field and n ≥ 2. Also we study the commuting graphs of some classical groups such as GL n (F) and SL n (F). We show that Γ(M n (F)) is a connected graph if and only if every field extension of F of degree n contains a proper intermediate field. We prove that apart from finitely many fields, a similar result is true for Γ(GL n (F)) and Γ(SL n (F)). Also we show that for two fields E and F and integers m, n ≥> 2, if Γ(M m (E)) ≅ Γ(M n (F)), then m = n and vertical bar E vertical bar = vertical bar F vertical bar. (author)

Graph-theoretical concepts and physicochemical data

Directory of Open Access Journals (Sweden)

Lionello Pogliani

2003-02-01

Full Text Available Graph theoretical concepts have been used to model the molecular polarizabilities of fifty-four organic derivatives, and the induced dipole moment of a set of fifty-seven organic compounds divided into three subsets. The starting point of these modeling strategies is the hydrogen-suppressed chemical graph and pseudograph of a molecule, which works very well for second row atoms. From these types of graphs a set of graph-theoretical basis indices, the molecular connectivity indices, can be derived and used to model properties and activities of molecules. With the aid of the molecular connectivity basis indices it is then possible to build higher-order descriptors. The problem of 'graph' encoding the contribution of the inner-core electrons of heteroatoms can here be solved with the aid of odd complete graphs, Kp-(p-odd. The use of these graph tools allow to draw an optimal modeling of the molecular polarizabilities and a satisfactory modeling of the induced dipole moment of a wide set of organic derivatives.

Graphs whose complement and square are isomorphic

DEFF Research Database (Denmark)

Pedersen, Anders Sune

2014-01-01

We study square-complementary graphs, that is, graphs whose complement and square are isomorphic. We prove several necessary conditions for a graph to be square-complementary, describe ways of building new square-complementary graphs from existing ones, construct infinite families of square-compl...

Graphs & digraphs

CERN Document Server

Chartrand, Gary; Zhang, Ping

2010-01-01

Gary Chartrand has influenced the world of Graph Theory for almost half a century. He has supervised more than a score of Ph.D. dissertations and written several books on the subject. The most widely known of these texts, Graphs and Digraphs, … has much to recommend it, with clear exposition, and numerous challenging examples [that] make it an ideal textbook for the advanced undergraduate or beginning graduate course. The authors have updated their notation to reflect the current practice in this still-growing area of study. By the authors' estimation, the 5th edition is approximately 50% longer than the 4th edition. … the legendary Frank Harary, author of the second graph theory text ever produced, is one of the figures profiled. His book was the standard in the discipline for several decades. Chartrand, Lesniak and Zhang have produced a worthy successor.-John T. Saccoman, MAA Reviews, June 2012 (This book is in the MAA's basic library list.)As with the earlier editions, the current text emphasizes clear...

Packing Degenerate Graphs Greedily

Czech Academy of Sciences Publication Activity Database

Allen, P.; Böttcher, J.; Hladký, J.; Piguet, Diana

2017-01-01

Roč. 61, August (2017), s. 45-51 ISSN 1571-0653 R&D Projects: GA ČR GJ16-07822Y Institutional support: RVO:67985807 Keywords : tree packing conjecture * graph packing * graph processes Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics

Continuous-time quantum walks on star graphs

International Nuclear Information System (INIS)

Salimi, S.

2009-01-01

In this paper, we investigate continuous-time quantum walk on star graphs. It is shown that quantum central limit theorem for a continuous-time quantum walk on star graphs for N-fold star power graph, which are invariant under the quantum component of adjacency matrix, converges to continuous-time quantum walk on K 2 graphs (complete graph with two vertices) and the probability of observing walk tends to the uniform distribution.

How edge-reinforced random walk arises naturally

NARCIS (Netherlands)

Rolles, S.W.W.

2003-01-01

We give a characterization of a modified edge-reinforced random walk in terms of certain partially exchangeable sequences. In particular, we obtain a characterization of an edge-reinforced random walk (introduced by Coppersmith and Diaconis) on a 2-edge-connected graph. Modifying the notion of

The Smallest Valid Extension-Based Efficient, Rare Graph Pattern Mining, Considering Length-Decreasing Support Constraints and Symmetry Characteristics of Graphs

Directory of Open Access Journals (Sweden)

Unil Yun

2016-05-01

Full Text Available Frequent graph mining has been proposed to find interesting patterns (i.e., frequent sub-graphs from databases composed of graph transaction data, which can effectively express complex and large data in the real world. In addition, various applications for graph mining have been suggested. Traditional graph pattern mining methods use a single minimum support threshold factor in order to check whether or not mined patterns are interesting. However, it is not a sufficient factor that can consider valuable characteristics of graphs such as graph sizes and features of graph elements. That is, previous methods cannot consider such important characteristics in their mining operations since they only use a fixed minimum support threshold in the mining process. For this reason, in this paper, we propose a novel graph mining algorithm that can consider various multiple, minimum support constraints according to the types of graph elements and changeable minimum support conditions, depending on lengths of graph patterns. In addition, the proposed algorithm performs in mining operations more efficiently because it can minimize duplicated operations and computational overheads by considering symmetry features of graphs. Experimental results provided in this paper demonstrate that the proposed algorithm outperforms previous mining approaches in terms of pattern generation, runtime and memory usage.

Relating zeta functions of discrete and quantum graphs

Science.gov (United States)

Harrison, Jonathan; Weyand, Tracy

2018-02-01

We write the spectral zeta function of the Laplace operator on an equilateral metric graph in terms of the spectral zeta function of the normalized Laplace operator on the corresponding discrete graph. To do this, we apply a relation between the spectrum of the Laplacian on a discrete graph and that of the Laplacian on an equilateral metric graph. As a by-product, we determine how the multiplicity of eigenvalues of the quantum graph, that are also in the spectrum of the graph with Dirichlet conditions at the vertices, depends on the graph geometry. Finally we apply the result to calculate the vacuum energy and spectral determinant of a complete bipartite graph and compare our results with those for a star graph, a graph in which all vertices are connected to a central vertex by a single edge.

Information Retrieval and Graph Analysis Approaches for Book Recommendation

Directory of Open Access Journals (Sweden)

Chahinez Benkoussas

2015-01-01

Full Text Available A combination of multiple information retrieval approaches is proposed for the purpose of book recommendation. In this paper, book recommendation is based on complex user's query. We used different theoretical retrieval models: probabilistic as InL2 (Divergence from Randomness model and language model and tested their interpolated combination. Graph analysis algorithms such as PageRank have been successful in Web environments. We consider the application of this algorithm in a new retrieval approach to related document network comprised of social links. We called Directed Graph of Documents (DGD a network constructed with documents and social information provided from each one of them. Specifically, this work tackles the problem of book recommendation in the context of INEX (Initiative for the Evaluation of XML retrieval Social Book Search track. A series of reranking experiments demonstrate that combining retrieval models yields significant improvements in terms of standard ranked retrieval metrics. These results extend the applicability of link analysis algorithms to different environments.

Information Retrieval and Graph Analysis Approaches for Book Recommendation.

Science.gov (United States)

Benkoussas, Chahinez; Bellot, Patrice

2015-01-01

A combination of multiple information retrieval approaches is proposed for the purpose of book recommendation. In this paper, book recommendation is based on complex user's query. We used different theoretical retrieval models: probabilistic as InL2 (Divergence from Randomness model) and language model and tested their interpolated combination. Graph analysis algorithms such as PageRank have been successful in Web environments. We consider the application of this algorithm in a new retrieval approach to related document network comprised of social links. We called Directed Graph of Documents (DGD) a network constructed with documents and social information provided from each one of them. Specifically, this work tackles the problem of book recommendation in the context of INEX (Initiative for the Evaluation of XML retrieval) Social Book Search track. A series of reranking experiments demonstrate that combining retrieval models yields significant improvements in terms of standard ranked retrieval metrics. These results extend the applicability of link analysis algorithms to different environments.

The One Universal Graph — a free and open graph database

International Nuclear Information System (INIS)

Ng, Liang S.; Champion, Corbin

2016-01-01

Recent developments in graph database mostly are huge projects involving big organizations, big operations and big capital, as the name Big Data attests. We proposed the concept of One Universal Graph (OUG) which states that all observable and known objects and concepts (physical, conceptual or digitally represented) can be connected with only one single graph; furthermore the OUG can be implemented with a very simple text file format with free software, capable of being executed on Android or smaller devices. As such the One Universal Graph Data Exchange (GOUDEX) modules can potentially be installed on hundreds of millions of Android devices and Intel compatible computers shipped annually. Coupled with its open nature and ability to connect to existing leading search engines and databases currently in operation, GOUDEX has the potential to become the largest and a better interface for users and programmers to interact with the data on the Internet. With a Web User Interface for users to use and program in native Linux environment, Free Crowdware implemented in GOUDEX can help inexperienced users learn programming with better organized documentation for free software, and is able to manage programmer's contribution down to a single line of code or a single variable in software projects. It can become the first practically realizable “Internet brain” on which a global artificial intelligence system can be implemented. Being practically free and open, One Universal Graph can have significant applications in robotics, artificial intelligence as well as social networks. (paper)

Recognition of fractal graphs

NARCIS (Netherlands)

Perepelitsa, VA; Sergienko, [No Value; Kochkarov, AM

1999-01-01

Definitions of prefractal and fractal graphs are introduced, and they are used to formulate mathematical models in different fields of knowledge. The topicality of fractal-graph recognition from the point of view, of fundamental improvement in the efficiency of the solution of algorithmic problems

Interactive Graph Layout of a Million Nodes

OpenAIRE

Peng Mi; Maoyuan Sun; Moeti Masiane; Yong Cao; Chris North

2016-01-01

Sensemaking of large graphs, specifically those with millions of nodes, is a crucial task in many fields. Automatic graph layout algorithms, augmented with real-time human-in-the-loop interaction, can potentially support sensemaking of large graphs. However, designing interactive algorithms to achieve this is challenging. In this paper, we tackle the scalability problem of interactive layout of large graphs, and contribute a new GPU-based force-directed layout algorithm that exploits graph to...

RATGRAPH: Computer Graphing of Rational Functions.

Science.gov (United States)

Minch, Bradley A.

1987-01-01

Presents an easy-to-use Applesoft BASIC program that graphs rational functions and any asymptotes that the functions might have. Discusses the nature of rational functions, graphing them manually, employing a computer to graph rational functions, and describes how the program works. (TW)

1 / n Expansion for the Number of Matchings on Regular Graphs and Monomer-Dimer Entropy

Science.gov (United States)

Pernici, Mario

2017-08-01

Using a 1 / n expansion, that is an expansion in descending powers of n, for the number of matchings in regular graphs with 2 n vertices, we study the monomer-dimer entropy for two classes of graphs. We study the difference between the extensive monomer-dimer entropy of a random r-regular graph G (bipartite or not) with 2 n vertices and the average extensive entropy of r-regular graphs with 2 n vertices, in the limit n → ∞. We find a series expansion for it in the numbers of cycles; with probability 1 it converges for dimer density p diverges as |ln(1-p)| for p → 1. In the case of regular lattices, we similarly expand the difference between the specific monomer-dimer entropy on a lattice and the one on the Bethe lattice; we write down its Taylor expansion in powers of p through the order 10, expressed in terms of the number of totally reducible walks which are not tree-like. We prove through order 6 that its expansion coefficients in powers of p are non-negative.

Graph algorithms in the titan toolkit.

Energy Technology Data Exchange (ETDEWEB)

McLendon, William Clarence, III; Wylie, Brian Neil

2009-10-01

Graph algorithms are a key component in a wide variety of intelligence analysis activities. The Graph-Based Informatics for Non-Proliferation and Counter-Terrorism project addresses the critical need of making these graph algorithms accessible to Sandia analysts in a manner that is both intuitive and effective. Specifically we describe the design and implementation of an open source toolkit for doing graph analysis, informatics, and visualization that provides Sandia with novel analysis capability for non-proliferation and counter-terrorism.

A Graph Calculus for Predicate Logic

Directory of Open Access Journals (Sweden)

Paulo A. S. Veloso

2013-03-01

Full Text Available We introduce a refutation graph calculus for classical first-order predicate logic, which is an extension of previous ones for binary relations. One reduces logical consequence to establishing that a constructed graph has empty extension, i. e. it represents bottom. Our calculus establishes that a graph has empty extension by converting it to a normal form, which is expanded to other graphs until we can recognize conflicting situations (equivalent to a formula and its negation.

Deep Learning with Dynamic Computation Graphs

OpenAIRE

Looks, Moshe; Herreshoff, Marcello; Hutchins, DeLesley; Norvig, Peter

2017-01-01

Neural networks that compute over graph structures are a natural fit for problems in a variety of domains, including natural language (parse trees) and cheminformatics (molecular graphs). However, since the computation graph has a different shape and size for every input, such networks do not directly support batched training or inference. They are also difficult to implement in popular deep learning libraries, which are based on static data-flow graphs. We introduce a technique called dynami...

Constructs for Programming with Graph Rewrites

OpenAIRE

Rodgers, Peter

2000-01-01

Graph rewriting is becoming increasingly popular as a method for programming with graph based data structures. We present several modifications to a basic serial graph rewriting paradigm and discuss how they improve coding programs in the Grrr graph rewriting programming language. The constructs we present are once only nodes, attractor nodes and single match rewrites. We illustrate the operation of the constructs by example. The advantages of adding these new rewrite modifiers is to reduce t...

Quantum chaos on discrete graphs

International Nuclear Information System (INIS)

Smilansky, Uzy

2007-01-01

Adapting a method developed for the study of quantum chaos on quantum (metric) graphs (Kottos and Smilansky 1997 Phys. Rev. Lett. 79 4794, Kottos and Smilansky 1999 Ann. Phys., NY 274 76), spectral ζ functions and trace formulae for discrete Laplacians on graphs are derived. This is achieved by expressing the spectral secular equation in terms of the periodic orbits of the graph and obtaining functions which belong to the class of ζ functions proposed originally by Ihara (1966 J. Mat. Soc. Japan 18 219) and expanded by subsequent authors (Stark and Terras 1996 Adv. Math. 121 124, Kotani and Sunada 2000 J. Math. Sci. Univ. Tokyo 7 7). Finally, a model of 'classical dynamics' on the discrete graph is proposed. It is analogous to the corresponding classical dynamics derived for quantum graphs (Kottos and Smilansky 1997 Phys. Rev. Lett. 79 4794, Kottos and Smilansky 1999 Ann. Phys., NY 274 76). (fast track communication)

RJSplot: Interactive Graphs with R.

Science.gov (United States)

Barrios, David; Prieto, Carlos

2018-03-01

Data visualization techniques provide new methods for the generation of interactive graphs. These graphs allow a better exploration and interpretation of data but their creation requires advanced knowledge of graphical libraries. Recent packages have enabled the integration of interactive graphs in R. However, R provides limited graphical packages that allow the generation of interactive graphs for computational biology applications. The present project has joined the analytical power of R with the interactive graphical features of JavaScript in a new R package (RJSplot). It enables the easy generation of interactive graphs in R, provides new visualization capabilities, and contributes to the advance of computational biology analytical methods. At present, 16 interactive graphics are available in RJSplot, such as the genome viewer, Manhattan plots, 3D plots, heatmaps, dendrograms, networks, and so on. The RJSplot package is freely available online at http://rjsplot.net. © 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Tailored graph ensembles as proxies or null models for real networks I: tools for quantifying structure

International Nuclear Information System (INIS)

Annibale, A; Coolen, A C C; Fernandes, L P; Fraternali, F; Kleinjung, J

2009-01-01

We study the tailoring of structured random graph ensembles to real networks, with the objective of generating precise and practical mathematical tools for quantifying and comparing network topologies macroscopically, beyond the level of degree statistics. Our family of ensembles can produce graphs with any prescribed degree distribution and any degree-degree correlation function; its control parameters can be calculated fully analytically, and as a result we can calculate (asymptotically) formulae for entropies and complexities and for information-theoretic distances between networks, expressed directly and explicitly in terms of their measured degree distribution and degree correlations.

Bipartite separability and nonlocal quantum operations on graphs

Science.gov (United States)

Dutta, Supriyo; Adhikari, Bibhas; Banerjee, Subhashish; Srikanth, R.

2016-07-01

In this paper we consider the separability problem for bipartite quantum states arising from graphs. Earlier it was proved that the degree criterion is the graph-theoretic counterpart of the familiar positive partial transpose criterion for separability, although there are entangled states with positive partial transpose for which the degree criterion fails. Here we introduce the concept of partially symmetric graphs and degree symmetric graphs by using the well-known concept of partial transposition of a graph and degree criteria, respectively. Thus, we provide classes of bipartite separable states of dimension m ×n arising from partially symmetric graphs. We identify partially asymmetric graphs that lack the property of partial symmetry. We develop a combinatorial procedure to create a partially asymmetric graph from a given partially symmetric graph. We show that this combinatorial operation can act as an entanglement generator for mixed states arising from partially symmetric graphs.

Algorithms and Data Structures for Graphs

DEFF Research Database (Denmark)

Rotenberg, Eva

are planar graphs, which are those that can be drawn on a piece of paper without any pair of edges crossing. For planar graphs where each edge can only be traversed in one direction, a fundamental question is whether there is a route from vertex A to vertex B in the graph. We show how such a graph can...... of the form: "Is there an edge such that all paths between A and B go via that edge?" and which can quickly be updated when edges are inserted or deleted. We further show how to represent a planar graph such that we can quickly update our representation when an edge is deleted, and such that questions...

On the nullity number of graphs

Directory of Open Access Journals (Sweden)

Mustapha Aouchiche

2017-10-01

Full Text Available The paper discusses bounds on the nullity number of graphs. It is proved in [B. Cheng and B. Liu, On the nullity of graphs. Electron. J. Linear Algebra 16 (2007 60--67] that $\\eta \\le n - D$, where $\\eta$, n and D denote the nullity number, the order and the diameter of a connected graph, respectively. We first give a necessary condition on the extremal graphs corresponding to that bound, and then we strengthen the bound itself using the maximum clique number. In addition, we prove bounds on the nullity using the number of pendant neighbors in a graph. One of those bounds is an improvement of a known bound involving the domination number.

The impact of home care nurses' numeracy and graph literacy on comprehension of visual display information: implications for dashboard design.

Science.gov (United States)

Dowding, Dawn; Merrill, Jacqueline A; Onorato, Nicole; Barrón, Yolanda; Rosati, Robert J; Russell, David

2018-02-01

To explore home care nurses' numeracy and graph literacy and their relationship to comprehension of visualized data. A multifactorial experimental design using online survey software. Nurses were recruited from 2 Medicare-certified home health agencies. Numeracy and graph literacy were measured using validated scales. Nurses were randomized to 1 of 4 experimental conditions. Each condition displayed data for 1 of 4 quality indicators, in 1 of 4 different visualized formats (bar graph, line graph, spider graph, table). A mixed linear model measured the impact of numeracy, graph literacy, and display format on data understanding. In all, 195 nurses took part in the study. They were slightly more numerate and graph literate than the general population. Overall, nurses understood information presented in bar graphs most easily (88% correct), followed by tables (81% correct), line graphs (77% correct), and spider graphs (41% correct). Individuals with low numeracy and low graph literacy had poorer comprehension of information displayed across all formats. High graph literacy appeared to enhance comprehension of data regardless of numeracy capabilities. Clinical dashboards are increasingly used to provide information to clinicians in visualized format, under the assumption that visual display reduces cognitive workload. Results of this study suggest that nurses' comprehension of visualized information is influenced by their numeracy, graph literacy, and the display format of the data. Individual differences in numeracy and graph literacy skills need to be taken into account when designing dashboard technology. © The Author 2017. Published by Oxford University Press on behalf of the American Medical Informatics Association. All rights reserved. For Permissions, please email: journals.permissions@oup.com

Graph Transforming Java Data

NARCIS (Netherlands)

de Mol, M.J.; Rensink, Arend; Hunt, James J.

This paper introduces an approach for adding graph transformation-based functionality to existing JAVA programs. The approach relies on a set of annotations to identify the intended graph structure, as well as on user methods to manipulate that structure, within the user’s own JAVA class

Graph processing platforms at scale: practices and experiences

Energy Technology Data Exchange (ETDEWEB)

Lim, Seung-Hwan [ORNL; Lee, Sangkeun (Matt) [ORNL; Brown, Tyler C [ORNL; Sukumar, Sreenivas R [ORNL; Ganesh, Gautam [ORNL

2015-01-01

Graph analysis unveils hidden associations of data in many phenomena and artifacts, such as road network, social networks, genomic information, and scientific collaboration. Unfortunately, a wide diversity in the characteristics of graphs and graph operations make it challenging to find a right combination of tools and implementation of algorithms to discover desired knowledge from the target data set. This study presents an extensive empirical study of three representative graph processing platforms: Pegasus, GraphX, and Urika. Each system represents a combination of options in data model, processing paradigm, and infrastructure. We benchmarked each platform using three popular graph operations, degree distribution, connected components, and PageRank over a variety of real-world graphs. Our experiments show that each graph processing platform shows different strength, depending the type of graph operations. While Urika performs the best in non-iterative operations like degree distribution, GraphX outputforms iterative operations like connected components and PageRank. In addition, we discuss challenges to optimize the performance of each platform over large scale real world graphs.

Generalized hypercube graph $\\Q_n(S$, graph products and self-orthogonal codes

Directory of Open Access Journals (Sweden)

Pani Seneviratne

2016-01-01

Full Text Available A generalized hypercube graph $\\Q_n(S$ has $\\F_{2}^{n}=\\{0,1\\}^n$ as the vertex set and two vertices being adjacent whenever their mutual Hamming distance belongs to $S$, where $n \\ge 1$ and $S\\subseteq \\{1,2,\\ldots, n\\}$. The graph $\\Q_n(\\{1\\}$ is the $n$-cube, usually denoted by $\\Q_n$.We study graph boolean products $G_1 = \\Q_n(S\\times \\Q_1, G_2 = \\Q_{n}(S\\wedge \\Q_1$, $G_3 = \\Q_{n}(S[\\Q_1]$ and show that binary codes from neighborhood designs of $G_1, G_2$ and $G_3$ are self-orthogonal for all choices of $n$ and $S$. More over, we show that the class of codes $C_1$ are self-dual. Further we find subgroups of the automorphism group of these graphs and use these subgroups to obtain PD-sets for permutation decoding. As an example we find a full error-correcting PD set for the binary $[32, 16, 8]$ extremal self-dual code.

Survey of Approaches to Generate Realistic Synthetic Graphs

Energy Technology Data Exchange (ETDEWEB)

Lim, Seung-Hwan [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Lee, Sangkeun [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Powers, Sarah S [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Shankar, Mallikarjun [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Imam, Neena [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

2016-10-01

A graph is a flexible data structure that can represent relationships between entities. As with other data analysis tasks, the use of realistic graphs is critical to obtaining valid research results. Unfortunately, using the actual ("real-world") graphs for research and new algorithm development is difficult due to the presence of sensitive information in the data or due to the scale of data. This results in practitioners developing algorithms and systems that employ synthetic graphs instead of real-world graphs. Generating realistic synthetic graphs that provide reliable statistical confidence to algorithmic analysis and system evaluation involves addressing technical hurdles in a broad set of areas. This report surveys the state of the art in approaches to generate realistic graphs that are derived from fitted graph models on real-world graphs.

Constructing Dense Graphs with Unique Hamiltonian Cycles

Science.gov (United States)

Lynch, Mark A. M.

2012-01-01

It is not difficult to construct dense graphs containing Hamiltonian cycles, but it is difficult to generate dense graphs that are guaranteed to contain a unique Hamiltonian cycle. This article presents an algorithm for generating arbitrarily large simple graphs containing "unique" Hamiltonian cycles. These graphs can be turned into dense graphs…

On some labelings of triangular snake and central graph of triangular snake graph

Science.gov (United States)

Agasthi, P.; Parvathi, N.

2018-04-01

A Triangular snake Tn is obtained from a path u 1 u 2 … u n by joining ui and u i+1 to a new vertex wi for 1≤i≤n‑1. A Central graph of Triangular snake C(T n ) is obtained by subdividing each edge of Tn exactly once and joining all the non adjacent vertices of Tn . In this paper the ways to construct square sum, square difference, Root Mean square, strongly Multiplicative, Even Mean and Odd Mean labeling for Triangular Snake and Central graph of Triangular Snake graphs are reported.

Orientations of infinite graphs with prescribed edge-connectivity

DEFF Research Database (Denmark)

Thomassen, Carsten

2016-01-01

We prove a decomposition result for locally finite graphs which can be used to extend results on edge-connectivity from finite to infinite graphs. It implies that every 4k-edge-connected graph G contains an immersion of some finite 2k-edge-connected Eulerian graph containing any prescribed vertex...... set (while planar graphs show that G need not containa subdivision of a simple finite graph of large edge-connectivity). Also, every 8k-edge connected infinite graph has a k-arc-connected orientation, as conjectured in 1989....

Genus Ranges of 4-Regular Rigid Vertex Graphs.

Science.gov (United States)

Buck, Dorothy; Dolzhenko, Egor; Jonoska, Nataša; Saito, Masahico; Valencia, Karin

2015-01-01

A rigid vertex of a graph is one that has a prescribed cyclic order of its incident edges. We study orientable genus ranges of 4-regular rigid vertex graphs. The (orientable) genus range is a set of genera values over all orientable surfaces into which a graph is embedded cellularly, and the embeddings of rigid vertex graphs are required to preserve the prescribed cyclic order of incident edges at every vertex. The genus ranges of 4-regular rigid vertex graphs are sets of consecutive integers, and we address two questions: which intervals of integers appear as genus ranges of such graphs, and what types of graphs realize a given genus range. For graphs with 2 n vertices ( n > 1), we prove that all intervals [ a, b ] for all a genus ranges. For graphs with 2 n - 1 vertices ( n ≥ 1), we prove that all intervals [ a, b ] for all a genus ranges. We also provide constructions of graphs that realize these ranges.

A new cluster algorithm for graphs

NARCIS (Netherlands)

S. van Dongen

1998-01-01

textabstractA new cluster algorithm for graphs called the emph{Markov Cluster algorithm ($MCL$ algorithm) is introduced. The graphs may be both weighted (with nonnegative weight) and directed. Let~$G$~be such a graph. The $MCL$ algorithm simulates flow in $G$ by first identifying $G$ in a

Chemical Graph Transformation with Stereo-Information

DEFF Research Database (Denmark)

Andersen, Jakob Lykke; Flamm, Christoph; Merkle, Daniel

2017-01-01

Double Pushout graph transformation naturally facilitates the modelling of chemical reactions: labelled undirected graphs model molecules and direct derivations model chemical reactions. However, the most straightforward modelling approach ignores the relative placement of atoms and their neighbo......Double Pushout graph transformation naturally facilitates the modelling of chemical reactions: labelled undirected graphs model molecules and direct derivations model chemical reactions. However, the most straightforward modelling approach ignores the relative placement of atoms...... and their neighbours in space. Stereoisomers of chemical compounds thus cannot be distinguished, even though their chemical activity may differ substantially. In this contribution we propose an extended chemical graph transformation system with attributes that encode information about local geometry. The modelling...... of graph transformation, but we here propose a framework that also allows for partially specified stereoinformation. While there are several stereochemical configurations to be considered, we focus here on the tetrahedral molecular shape, and suggest general principles for how to treat all other chemically...

Large-Scale Graph Processing Using Apache Giraph

KAUST Repository

Sakr, Sherif

2017-01-07

This book takes its reader on a journey through Apache Giraph, a popular distributed graph processing platform designed to bring the power of big data processing to graph data. Designed as a step-by-step self-study guide for everyone interested in large-scale graph processing, it describes the fundamental abstractions of the system, its programming models and various techniques for using the system to process graph data at scale, including the implementation of several popular and advanced graph analytics algorithms.

Large-Scale Graph Processing Using Apache Giraph

KAUST Repository

Sakr, Sherif; Orakzai, Faisal Moeen; Abdelaziz, Ibrahim; Khayyat, Zuhair

2017-01-01

This book takes its reader on a journey through Apache Giraph, a popular distributed graph processing platform designed to bring the power of big data processing to graph data. Designed as a step-by-step self-study guide for everyone interested in large-scale graph processing, it describes the fundamental abstractions of the system, its programming models and various techniques for using the system to process graph data at scale, including the implementation of several popular and advanced graph analytics algorithms.

Graph Algorithm Animation with Grrr

OpenAIRE

Rodgers, Peter; Vidal, Natalia

2000-01-01

We discuss geometric positioning, highlighting of visited nodes and user defined highlighting that form the algorithm animation facilities in the Grrr graph rewriting programming language. The main purpose of animation was initially for the debugging and profiling of Grrr code, but recently it has been extended for the purpose of teaching algorithms to undergraduate students. The animation is restricted to graph based algorithms such as graph drawing, list manipulation or more traditional gra...

Central Limit Theorem for Exponentially Quasi-local Statistics of Spin Models on Cayley Graphs

Science.gov (United States)

Reddy, Tulasi Ram; Vadlamani, Sreekar; Yogeshwaran, D.

2018-04-01

Central limit theorems for linear statistics of lattice random fields (including spin models) are usually proven under suitable mixing conditions or quasi-associativity. Many interesting examples of spin models do not satisfy mixing conditions, and on the other hand, it does not seem easy to show central limit theorem for local statistics via quasi-associativity. In this work, we prove general central limit theorems for local statistics and exponentially quasi-local statistics of spin models on discrete Cayley graphs with polynomial growth. Further, we supplement these results by proving similar central limit theorems for random fields on discrete Cayley graphs taking values in a countable space, but under the stronger assumptions of α -mixing (for local statistics) and exponential α -mixing (for exponentially quasi-local statistics). All our central limit theorems assume a suitable variance lower bound like many others in the literature. We illustrate our general central limit theorem with specific examples of lattice spin models and statistics arising in computational topology, statistical physics and random networks. Examples of clustering spin models include quasi-associated spin models with fast decaying covariances like the off-critical Ising model, level sets of Gaussian random fields with fast decaying covariances like the massive Gaussian free field and determinantal point processes with fast decaying kernels. Examples of local statistics include intrinsic volumes, face counts, component counts of random cubical complexes while exponentially quasi-local statistics include nearest neighbour distances in spin models and Betti numbers of sub-critical random cubical complexes.

My Bar Graph Tells a Story

Science.gov (United States)

McMillen, Sue; McMillen, Beth

2010-01-01

Connecting stories to qualitative coordinate graphs has been suggested as an effective instructional strategy. Even students who are able to "create" bar graphs may struggle to correctly "interpret" them. Giving children opportunities to work with qualitative graphs can help them develop the skills to interpret, describe, and compare information…

An intersection graph of straight lines

DEFF Research Database (Denmark)

Thomassen, Carsten

2002-01-01

G. Ehrlich, S. Even, and R.E. Tarjan conjectured that the graph obtained from a complete 3 partite graph K4,4,4 by deleting the edges of four disjoint triangles is not the intersection graph of straight line segments in the plane. We show that it is....

Trajectories entropy in dynamical graphs with memory

Directory of Open Access Journals (Sweden)

Francesco eCaravelli

2016-04-01

Full Text Available In this paper we investigate the application of non-local graph entropy to evolving and dynamical graphs. The measure is based upon the notion of Markov diffusion on a graph, and relies on the entropy applied to trajectories originating at a specific node. In particular, we study the model of reinforcement-decay graph dynamics, which leads to scale free graphs. We find that the node entropy characterizes the structure of the network in the two parameter phase-space describing the dynamical evolution of the weighted graph. We then apply an adapted version of the entropy measure to purely memristive circuits. We provide evidence that meanwhile in the case of DC voltage the entropy based on the forward probability is enough to characterize the graph properties, in the case of AC voltage generators one needs to consider both forward and backward based transition probabilities. We provide also evidence that the entropy highlights the self-organizing properties of memristive circuits, which re-organizes itself to satisfy the symmetries of the underlying graph.

On revealing graph cycles via boundary measurements

International Nuclear Information System (INIS)

Belishev, M I; Wada, N

2009-01-01

This paper deals with boundary value inverse problems on a metric graph, the structure of the graph being assumed unknown. The question under consideration is how to detect from the dynamical and/or spectral inverse data whether the graph contains cycles (is not a tree). For any graph Ω, the dynamical as well as spectral boundary inverse data determine the so-called wave diameter d w : H -1 (Ω) → R defined on functionals supported in the graph. The known fact is that if Ω is a tree then d w ≥ 0 holds and, in this case, the inverse data determine Ω up to isometry. A graph Ω is said to be coordinate if the functions {dist Ω (., γ)} γin∂Ω constitute a coordinate system on Ω. For such graphs, we propose a procedure, which reveals the presence/absence of cycles. The hypothesis is that Ω contains cycles if and only if d w takes negative values. We do not justify this hypothesis in the general case but reduce it to a certain special class of graphs (suns)

OPEX: Optimized Eccentricity Computation in Graphs

Energy Technology Data Exchange (ETDEWEB)

Henderson, Keith [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

2011-11-14

Real-world graphs have many properties of interest, but often these properties are expensive to compute. We focus on eccentricity, radius and diameter in this work. These properties are useful measures of the global connectivity patterns in a graph. Unfortunately, computing eccentricity for all nodes is O(n2) for a graph with n nodes. We present OPEX, a novel combination of optimizations which improves computation time of these properties by orders of magnitude in real-world experiments on graphs of many different sizes. We run OPEX on graphs with up to millions of links. OPEX gives either exact results or bounded approximations, unlike its competitors which give probabilistic approximations or sacrifice node-level information (eccentricity) to compute graphlevel information (diameter).

Pixels to Graphs by Associative Embedding

KAUST Repository

Newell, Alejandro

2017-06-22

Graphs are a useful abstraction of image content. Not only can graphs represent details about individual objects in a scene but they can capture the interactions between pairs of objects. We present a method for training a convolutional neural network such that it takes in an input image and produces a full graph. This is done end-to-end in a single stage with the use of associative embeddings. The network learns to simultaneously identify all of the elements that make up a graph and piece them together. We benchmark on the Visual Genome dataset, and report a Recall@50 of 9.7% compared to the prior state-of-the-art at 3.4%, a nearly threefold improvement on the challenging task of scene graph generation.

Probabilistic graphs as a conceptual and computational tool in hydrology and water management

Science.gov (United States)

Schoups, Gerrit

2014-05-01

Originally developed in the fields of machine learning and artificial intelligence, probabilistic graphs constitute a general framework for modeling complex systems in the presence of uncertainty. The framework consists of three components: 1. Representation of the model as a graph (or network), with nodes depicting random variables in the model (e.g. parameters, states, etc), which are joined together by factors. Factors are local probabilistic or deterministic relations between subsets of variables, which, when multiplied together, yield the joint distribution over all variables. 2. Consistent use of probability theory for quantifying uncertainty, relying on basic rules of probability for assimilating data into the model and expressing unknown variables as a function of observations (via the posterior distribution). 3. Efficient, distributed approximation of the posterior distribution using general-purpose algorithms that exploit model structure encoded in the graph. These attributes make probabilistic graphs potentially useful as a conceptual and computational tool in hydrology and water management (and beyond). Conceptually, they can provide a common framework for existing and new probabilistic modeling approaches (e.g. by drawing inspiration from other fields of application), while computationally they can make probabilistic inference feasible in larger hydrological models. The presentation explores, via examples, some of these benefits.

A faithful functor among algebras and graphs

OpenAIRE

Falcón Ganfornina, Óscar Jesús; Falcón Ganfornina, Raúl Manuel; Núñez Valdés, Juan; Pacheco Martínez, Ana María; Villar Liñán, María Trinidad; Vigo Aguiar, Jesús (Coordinador)

2016-01-01

The problem of identifying a functor between the categories of algebras and graphs is currently open. Based on a known algorithm that identifies isomorphisms of Latin squares with isomorphism of vertex-colored graphs, we describe here a pair of graphs that enable us to find a faithful functor between finite-dimensional algebras over finite fields and these graphs.

GraphCrunch 2: Software tool for network modeling, alignment and clustering.

Science.gov (United States)

Kuchaiev, Oleksii; Stevanović, Aleksandar; Hayes, Wayne; Pržulj, Nataša

2011-01-19

Recent advancements in experimental biotechnology have produced large amounts of protein-protein interaction (PPI) data. The topology of PPI networks is believed to have a strong link to their function. Hence, the abundance of PPI data for many organisms stimulates the development of computational techniques for the modeling, comparison, alignment, and clustering of networks. In addition, finding representative models for PPI networks will improve our understanding of the cell just as a model of gravity has helped us understand planetary motion. To decide if a model is representative, we need quantitative comparisons of model networks to real ones. However, exact network comparison is computationally intractable and therefore several heuristics have been used instead. Some of these heuristics are easily computable "network properties," such as the degree distribution, or the clustering coefficient. An important special case of network comparison is the network alignment problem. Analogous to sequence alignment, this problem asks to find the "best" mapping between regions in two networks. It is expected that network alignment might have as strong an impact on our understanding of biology as sequence alignment has had. Topology-based clustering of nodes in PPI networks is another example of an important network analysis problem that can uncover relationships between interaction patterns and phenotype. We introduce the GraphCrunch 2 software tool, which addresses these problems. It is a significant extension of GraphCrunch which implements the most popular random network models and compares them with the data networks with respect to many network properties. Also, GraphCrunch 2 implements the GRAph ALigner algorithm ("GRAAL") for purely topological network alignment. GRAAL can align any pair of networks and exposes large, dense, contiguous regions of topological and functional similarities far larger than any other existing tool. Finally, GraphCruch 2 implements an

GraphCrunch 2: Software tool for network modeling, alignment and clustering

Directory of Open Access Journals (Sweden)

Hayes Wayne

2011-01-01

Full Text Available Abstract Background Recent advancements in experimental biotechnology have produced large amounts of protein-protein interaction (PPI data. The topology of PPI networks is believed to have a strong link to their function. Hence, the abundance of PPI data for many organisms stimulates the development of computational techniques for the modeling, comparison, alignment, and clustering of networks. In addition, finding representative models for PPI networks will improve our understanding of the cell just as a model of gravity has helped us understand planetary motion. To decide if a model is representative, we need quantitative comparisons of model networks to real ones. However, exact network comparison is computationally intractable and therefore several heuristics have been used instead. Some of these heuristics are easily computable "network properties," such as the degree distribution, or the clustering coefficient. An important special case of network comparison is the network alignment problem. Analogous to sequence alignment, this problem asks to find the "best" mapping between regions in two networks. It is expected that network alignment might have as strong an impact on our understanding of biology as sequence alignment has had. Topology-based clustering of nodes in PPI networks is another example of an important network analysis problem that can uncover relationships between interaction patterns and phenotype. Results We introduce the GraphCrunch 2 software tool, which addresses these problems. It is a significant extension of GraphCrunch which implements the most popular random network models and compares them with the data networks with respect to many network properties. Also, GraphCrunch 2 implements the GRAph ALigner algorithm ("GRAAL" for purely topological network alignment. GRAAL can align any pair of networks and exposes large, dense, contiguous regions of topological and functional similarities far larger than any other

Cellular Automata on Graphs: Topological Properties of ER Graphs Evolved towards Low-Entropy Dynamics

Directory of Open Access Journals (Sweden)

Marc-Thorsten Hütt

2012-06-01

Full Text Available Cellular automata (CA are a remarkably  efficient tool for exploring general properties of complex systems and spatiotemporal patterns arising from local rules. Totalistic cellular automata,  where the update  rules depend  only on the density of neighboring states, are at the same time a versatile  tool for exploring  dynamical  processes on graphs. Here we briefly review our previous results on cellular automata on graphs, emphasizing some systematic relationships between network architecture and dynamics identified in this way. We then extend the investigation  towards graphs obtained in a simulated-evolution procedure, starting from Erdő s–Rényi (ER graphs and selecting for low entropies of the CA dynamics. Our key result is a strong association of low Shannon entropies with a broadening of the graph’s degree distribution.

The color space of a graph

DEFF Research Database (Denmark)

Jensen, T.R.; Thomassen, Carsten

2000-01-01

If k is a prime power, and G is a graph with n vertices, then a k-coloring of G may be considered as a vector in GF(k)(n). We prove that the subspace of GF(3)(n) spanned by all 3-colorings of a planar triangle-free graph with n vertices has dimension n. In particular, any such graph has at least n...... - 1 nonequivalent 3-colorings, and the addition of any edge or any vertex of degree 3 results in a 3-colorable graph. (C) 2000 John Wiley & Sons, Inc....

Box graphs and resolutions I

Directory of Open Access Journals (Sweden)

Andreas P. Braun

2016-04-01

Full Text Available Box graphs succinctly and comprehensively characterize singular fibers of elliptic fibrations in codimension two and three, as well as flop transitions connecting these, in terms of representation theoretic data. We develop a framework that provides a systematic map between a box graph and a crepant algebraic resolution of the singular elliptic fibration, thus allowing an explicit construction of the fibers from a singular Weierstrass or Tate model. The key tool is what we call a fiber face diagram, which shows the relevant information of a (partial toric triangulation and allows the inclusion of more general algebraic blowups. We shown that each such diagram defines a sequence of weighted algebraic blowups, thus providing a realization of the fiber defined by the box graph in terms of an explicit resolution. We show this correspondence explicitly for the case of SU(5 by providing a map between box graphs and fiber faces, and thereby a sequence of algebraic resolutions of the Tate model, which realizes each of the box graphs.

Forbidden Structures for Planar Perfect Consecutively Colourable Graphs

Directory of Open Access Journals (Sweden)

Borowiecka-Olszewska Marta

2017-05-01

Full Text Available A consecutive colouring of a graph is a proper edge colouring with posi- tive integers in which the colours of edges incident with each vertex form an interval of integers. The idea of this colouring was introduced in 1987 by Asratian and Kamalian under the name of interval colouring. Sevast- janov showed that the corresponding decision problem is NP-complete even restricted to the class of bipartite graphs. We focus our attention on the class of consecutively colourable graphs whose all induced subgraphs are consecutively colourable, too. We call elements of this class perfect consecutively colourable to emphasise the conceptual similarity to perfect graphs. Obviously, the class of perfect consecutively colourable graphs is induced hereditary, so it can be characterized by the family of induced forbidden graphs. In this work we give a necessary and sufficient conditions that must be satisfied by the generalized Sevastjanov rosette to be an induced forbid- den graph for the class of perfect consecutively colourable graphs. Along the way, we show the exact values of the deficiency of all generalized Sevastjanov rosettes, which improves the earlier known estimating result. It should be mentioned that the deficiency of a graph measures its closeness to the class of consecutively colourable graphs. We motivate the investigation of graphs considered here by showing their connection to the class of planar perfect consecutively colourable graphs.

47 CFR 80.761 - Conversion graphs.

Science.gov (United States)

2010-10-01

... MARITIME SERVICES Standards for Computing Public Coast Station VHF Coverage § 80.761 Conversion graphs. The following graphs must be employed where conversion from one to the other of the indicated types of units is... 47 Telecommunication 5 2010-10-01 2010-10-01 false Conversion graphs. 80.761 Section 80.761...

A Study on The Mixture of Exponentiated-Weibull Distribution

Directory of Open Access Journals (Sweden)

Adel Tawfik Elshahat

2016-12-01

Full Text Available Mixtures of measures or distributions occur frequently in the theory and applications of probability and statistics. In the simplest case it may, for example, be reasonable to assume that one is dealing with the mixture in given proportions of a finite number of normal populations with different means or variances. The mixture parameter may also be denumerable infinite, as in the theory of sums of a random number of random variables, or continuous, as in the compound Poisson distribution. The use of finite mixture distributions, to control for unobserved heterogeneity, has become increasingly popular among those estimating dynamic discrete choice models. One of the barriers to using mixture models is that parameters that could previously be estimated in stages must now be estimated jointly: using mixture distributions destroys any additive reparability of the log likelihood function. In this thesis, the maximum likelihood estimators have been obtained for the parameters of the mixture of exponentiated Weibull distribution when sample is available from censoring scheme. The maximum likelihood estimators of the parameters and the asymptotic variance covariance matrix have been also obtained. A numerical illustration for these new results is given.

Building Scalable Knowledge Graphs for Earth Science

Science.gov (United States)

Ramachandran, Rahul; Maskey, Manil; Gatlin, Patrick; Zhang, Jia; Duan, Xiaoyi; Miller, J. J.; Bugbee, Kaylin; Christopher, Sundar; Freitag, Brian

2017-01-01

Knowledge Graphs link key entities in a specific domain with other entities via relationships. From these relationships, researchers can query knowledge graphs for probabilistic recommendations to infer new knowledge. Scientific papers are an untapped resource which knowledge graphs could leverage to accelerate research discovery. Goal: Develop an end-to-end (semi) automated methodology for constructing Knowledge Graphs for Earth Science.

On the diameter of dot-critical graphs

Directory of Open Access Journals (Sweden)

Doost Ali Mojdeh

2009-01-01

Full Text Available A graph G is \\(k\\-dot-critical (totaly \\(k\\-dot-critical if \\(G\\ is dot-critical (totaly dot-critical and the domination number is \\(k\\. In the paper [T. Burtona, D. P. Sumner, Domination dot-critical graphs, Discrete Math, 306 (2006, 11-18] the following question is posed: What are the best bounds for the diameter of a \\(k\\-dot-critical graph and a totally \\(k\\-dot-critical graph \\(G\\ with no critical vertices for \\(k \\geq 4\\? We find the best bound for the diameter of a \\(k\\-dot-critical graph, where \\(k \\in\\{4,5,6\\}\\ and we give a family of \\(k\\-dot-critical graphs (with no critical vertices with sharp diameter \\(2k-3\\ for even \\(k \\geq 4\\.

Topological properties of random wireless networks

Indian Academy of Sciences (India)

Wireless networks in which the node locations are random are best modelled as random geometric graphs (RGGs). In addition to their extensive application in the modelling of wireless networks, RGGs find many new applications and are being studied in their own right. In this paper we first provide a brief introduction to the ...

Intrinsic intensity fluctuations in random lasers

International Nuclear Information System (INIS)

Molen, Karen L. van der; Mosk, Allard P.; Lagendijk, Ad

2006-01-01

We present a quantitative experimental and theoretical study of intensity fluctuations in the emitted light of a random laser that has different realizations of disorder for every pump pulse. A model that clarifies these intrinsic fluctuations is developed. We describe the output versus input power graphs of the random laser with an effective spontaneous emission factor (β factor)

Graph anomalies in cyber communications

Energy Technology Data Exchange (ETDEWEB)

Vander Wiel, Scott A [Los Alamos National Laboratory; Storlie, Curtis B [Los Alamos National Laboratory; Sandine, Gary [Los Alamos National Laboratory; Hagberg, Aric A [Los Alamos National Laboratory; Fisk, Michael [Los Alamos National Laboratory

2011-01-11

Enterprises monitor cyber traffic for viruses, intruders and stolen information. Detection methods look for known signatures of malicious traffic or search for anomalies with respect to a nominal reference model. Traditional anomaly detection focuses on aggregate traffic at central nodes or on user-level monitoring. More recently, however, traffic is being viewed more holistically as a dynamic communication graph. Attention to the graph nature of the traffic has expanded the types of anomalies that are being sought. We give an overview of several cyber data streams collected at Los Alamos National Laboratory and discuss current work in modeling the graph dynamics of traffic over the network. We consider global properties and local properties within the communication graph. A method for monitoring relative entropy on multiple correlated properties is discussed in detail.

Graphs, groups and surfaces

CERN Document Server

White, AT

1985-01-01

The field of topological graph theory has expanded greatly in the ten years since the first edition of this book appeared. The original nine chapters of this classic work have therefore been revised and updated. Six new chapters have been added, dealing with: voltage graphs, non-orientable imbeddings, block designs associated with graph imbeddings, hypergraph imbeddings, map automorphism groups and change ringing.Thirty-two new problems have been added to this new edition, so that there are now 181 in all; 22 of these have been designated as ``difficult'''' and 9 as ``unsolved''''. Three of the four unsolved problems from the first edition have been solved in the ten years between editions; they are now marked as ``difficult''''.

Subdominant pseudoultrametric on graphs

Energy Technology Data Exchange (ETDEWEB)

Dovgoshei, A A; Petrov, E A [Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Donetsk (Ukraine)

2013-08-31

Let (G,w) be a weighted graph. We find necessary and sufficient conditions under which the weight w:E(G)→R{sup +} can be extended to a pseudoultrametric on V(G), and establish a criterion for the uniqueness of such an extension. We demonstrate that (G,w) is a complete k-partite graph, for k≥2, if and only if for any weight that can be extended to a pseudoultrametric, among all such extensions one can find the least pseudoultrametric consistent with w. We give a structural characterization of graphs for which the subdominant pseudoultrametric is an ultrametric for any strictly positive weight that can be extended to a pseudoultrametric. Bibliography: 14 titles.

Equitable Colorings Of Corona Multiproducts Of Graphs

Directory of Open Access Journals (Sweden)

Furmánczyk Hanna

2017-11-01

Full Text Available A graph is equitably k-colorable if its vertices can be partitioned into k independent sets in such a way that the numbers of vertices in any two sets differ by at most one. The smallest k for which such a coloring exists is known as the equitable chromatic number of G and denoted by =(G. It is known that the problem of computation of =(G is NP-hard in general and remains so for corona graphs. In this paper we consider the same model of coloring in the case of corona multiproducts of graphs. In particular, we obtain some results regarding the equitable chromatic number for the l-corona product G ◦l H, where G is an equitably 3- or 4-colorable graph and H is an r-partite graph, a cycle or a complete graph. Our proofs are mostly constructive in that they lead to polynomial algorithms for equitable coloring of such graph products provided that there is given an equitable coloring of G. Moreover, we confirm the Equitable Coloring Conjecture for corona products of such graphs. This paper extends the results from [H. Furmánczyk, K. Kaliraj, M. Kubale and V.J. Vivin, Equitable coloring of corona products of graphs, Adv. Appl. Discrete Math. 11 (2013 103–120].

Topical anesthesia with eutetic mixture of local anesthetics cream in vasectomy: 2 randomized trials

DEFF Research Database (Denmark)

Honnens de Lichtenberg, M; Krogh, J; Rye, B

1992-01-01

Two paired randomized trials testing topical anesthesia with a eutetic mixture of local anesthetics (EMLA cream*) in vasectomy were performed. In 1 trial EMLA cream was applied on 1 side of the scrotum, while infiltration anesthesia into the skin and subcutaneous tissue with mepivacaine was used...... on the contralateral side. All but 1 of the 13 patients (p less than 0.05) preferred infiltration anesthesia because of pain as the incision reached the subcutaneous tissue. In the other trial 29 patients received EMLA cream on 1 side of the scrotum before bilateral mepivacaine infiltration. There was significantly...... less pain on the sides with the anesthetic cream (p less than 0.001). Many patients would pay the price of the cream. In conclusion, EMLA cream cannot replace but it can supplement infiltration anesthesia during vasectomy....

Sphere and dot product representations of graphs

NARCIS (Netherlands)

R.J. Kang (Ross); T. Müller (Tobias)

2012-01-01

textabstractA graph $G$ is a $k$-sphere graph if there are $k$-dimensional real vectors $v_1,\\dots,v_n$ such that $ij\\in E(G)$ if and only if the distance between $v_i$ and $v_j$ is at most $1$. A graph $G$ is a $k$-dot product graph if there are $k$-dimensional real vectors $v_1,\\dots,v_n$ such

Graph Query Portal

OpenAIRE

Dayal, Amit; Brock, David

2018-01-01

Prashant Chandrasekar, a lead developer for the Social Interactome project, has tasked the team with creating a graph representation of the data collected from the social networks involved in that project. The data is currently stored in a MySQL database. The client requested that the graph database be Cayley, but after a literature review, Neo4j was chosen. The reasons for this shift will be explained in the design section. Secondarily, the team was tasked with coming up with three scena...

Efficient Training Methods for Conditional Random Fields

National Research Council Canada - National Science Library

Sutton, Charles A

2008-01-01

.... In this thesis, I investigate efficient training methods for conditional random fields with complex graphical structure, focusing on local methods which avoid propagating information globally along the graph...

Consensus pursuit of heterogeneous multi-agent systems under a directed acyclic graph

Science.gov (United States)

Yan, Jing; Guan, Xin-Ping; Luo, Xiao-Yuan

2011-04-01

This paper is concerned with the cooperative target pursuit problem by multiple agents based on directed acyclic graph. The target appears at a random location and moves only when sensed by the agents, and agents will pursue the target once they detect its existence. Since the ability of each agent may be different, we consider the heterogeneous multi-agent systems. According to the topology of the multi-agent systems, a novel consensus-based control law is proposed, where the target and agents are modeled as a leader and followers, respectively. Based on Mason's rule and signal flow graph analysis, the convergence conditions are provided to show that the agents can catch the target in a finite time. Finally, simulation studies are provided to verify the effectiveness of the proposed approach.

An Association-Oriented Partitioning Approach for Streaming Graph Query

Directory of Open Access Journals (Sweden)

Yun Hao

2017-01-01

Full Text Available The volumes of real-world graphs like knowledge graph are increasing rapidly, which makes streaming graph processing a hot research area. Processing graphs in streaming setting poses significant challenges from different perspectives, among which graph partitioning method plays a key role. Regarding graph query, a well-designed partitioning method is essential for achieving better performance. Existing offline graph partitioning methods often require full knowledge of the graph, which is not possible during streaming graph processing. In order to handle this problem, we propose an association-oriented streaming graph partitioning method named Assc. This approach first computes the rank values of vertices with a hybrid approximate PageRank algorithm. After splitting these vertices with an adapted variant affinity propagation algorithm, the process order on vertices in the sliding window can be determined. Finally, according to the level of these vertices and their association, the partition where the vertices should be distributed is decided. We compare its performance with a set of streaming graph partition methods and METIS, a widely adopted offline approach. The results show that our solution can partition graphs with hundreds of millions of vertices in streaming setting on a large collection of graph datasets and our approach outperforms other graph partitioning methods.

A comparative study of applying Mason’s Rule in the case of flow-graphs and bond-graphs

Directory of Open Access Journals (Sweden)

Adriana Grava

2009-05-01

Full Text Available The paper presents two methods to analyzethe electric circuits using the flow-graphs and thebond-graphs studying the differences between thesemethods.As it can be noticed, the two methods are totallydifferent; their common point being Mason’s rule thatis applied in both cases but it is applied differently foreach type of graphs.

An algebraic approach to graph codes

DEFF Research Database (Denmark)

Pinero, Fernando

This thesis consists of six chapters. The first chapter, contains a short introduction to coding theory in which we explain the coding theory concepts we use. In the second chapter, we present the required theory for evaluation codes and also give an example of some fundamental codes in coding...... theory as evaluation codes. Chapter three consists of the introduction to graph based codes, such as Tanner codes and graph codes. In Chapter four, we compute the dimension of some graph based codes with a result combining graph based codes and subfield subcodes. Moreover, some codes in chapter four...

The STAPL Parallel Graph Library

KAUST Repository

Harshvardhan,; Fidel, Adam; Amato, Nancy M.; Rauchwerger, Lawrence

2013-01-01

This paper describes the stapl Parallel Graph Library, a high-level framework that abstracts the user from data-distribution and parallelism details and allows them to concentrate on parallel graph algorithm development. It includes a customizable

Coloring and The Lonely Graph

OpenAIRE

Rabern, Landon

2007-01-01

We improve upper bounds on the chromatic number proven independently in \\cite{reedNote} and \\cite{ingo}. Our main lemma gives a sufficient condition for two paths in graph to be completely joined. Using this, we prove that if a graph has an optimal coloring with more than $\\frac{\\omega}{2}$ singleton color classes, then it satisfies $\\chi \\leq \\frac{\\omega + \\Delta + 1}{2}$. It follows that a graph satisfying $n - \\Delta < \\alpha + \\frac{\\omega - 1}{2}$ must also satisfy $\\chi \\leq \\frac{\\ome...

Graph Mining Meets the Semantic Web

Energy Technology Data Exchange (ETDEWEB)

Lee, Sangkeun (Matt) [ORNL; Sukumar, Sreenivas R [ORNL; Lim, Seung-Hwan [ORNL

2015-01-01

The Resource Description Framework (RDF) and SPARQL Protocol and RDF Query Language (SPARQL) were introduced about a decade ago to enable flexible schema-free data interchange on the Semantic Web. Today, data scientists use the framework as a scalable graph representation for integrating, querying, exploring and analyzing data sets hosted at different sources. With increasing adoption, the need for graph mining capabilities for the Semantic Web has emerged. We address that need through implementation of three popular iterative Graph Mining algorithms (Triangle count, Connected component analysis, and PageRank). We implement these algorithms as SPARQL queries, wrapped within Python scripts. We evaluate the performance of our implementation on 6 real world data sets and show graph mining algorithms (that have a linear-algebra formulation) can indeed be unleashed on data represented as RDF graphs using the SPARQL query interface.

A model of language inflection graphs

Science.gov (United States)

Fukś, Henryk; Farzad, Babak; Cao, Yi

2014-01-01

Inflection graphs are highly complex networks representing relationships between inflectional forms of words in human languages. For so-called synthetic languages, such as Latin or Polish, they have particularly interesting structure due to the abundance of inflectional forms. We construct the simplest form of inflection graphs, namely a bipartite graph in which one group of vertices corresponds to dictionary headwords and the other group to inflected forms encountered in a given text. We, then, study projection of this graph on the set of headwords. The projection decomposes into a large number of connected components, to be called word groups. Distribution of sizes of word group exhibits some remarkable properties, resembling cluster distribution in a lattice percolation near the critical point. We propose a simple model which produces graphs of this type, reproducing the desired component distribution and other topological features.

Incremental Frequent Subgraph Mining on Large Evolving Graphs

KAUST Repository

Abdelhamid, Ehab

2017-08-22

Frequent subgraph mining is a core graph operation used in many domains, such as graph data management and knowledge exploration, bioinformatics and security. Most existing techniques target static graphs. However, modern applications, such as social networks, utilize large evolving graphs. Mining these graphs using existing techniques is infeasible, due to the high computational cost. In this paper, we propose IncGM+, a fast incremental approach for continuous frequent subgraph mining problem on a single large evolving graph. We adapt the notion of “fringe” to the graph context, that is the set of subgraphs on the border between frequent and infrequent subgraphs. IncGM+ maintains fringe subgraphs and exploits them to prune the search space. To boost the efficiency, we propose an efficient index structure to maintain selected embeddings with minimal memory overhead. These embeddings are utilized to avoid redundant expensive subgraph isomorphism operations. Moreover, the proposed system supports batch updates. Using large real-world graphs, we experimentally verify that IncGM+ outperforms existing methods by up to three orders of magnitude, scales to much larger graphs and consumes less memory.

Smooth Bundling of Large Streaming and Sequence Graphs

NARCIS (Netherlands)

Hurter, C.; Ersoy, O.; Telea, A.

2013-01-01

Dynamic graphs are increasingly pervasive in modern information systems. However, understanding how a graph changes in time is difficult. We present here two techniques for simplified visualization of dynamic graphs using edge bundles. The first technique uses a recent image-based graph bundling

The random projection method

CERN Document Server

Vempala, Santosh S

2005-01-01

Random projection is a simple geometric technique for reducing the dimensionality of a set of points in Euclidean space while preserving pairwise distances approximately. The technique plays a key role in several breakthrough developments in the field of algorithms. In other cases, it provides elegant alternative proofs. The book begins with an elementary description of the technique and its basic properties. Then it develops the method in the context of applications, which are divided into three groups. The first group consists of combinatorial optimization problems such as maxcut, graph coloring, minimum multicut, graph bandwidth and VLSI layout. Presented in this context is the theory of Euclidean embeddings of graphs. The next group is machine learning problems, specifically, learning intersections of halfspaces and learning large margin hypotheses. The projection method is further refined for the latter application. The last set consists of problems inspired by information retrieval, namely, nearest neig...

Open Graphs and Computational Reasoning

Directory of Open Access Journals (Sweden)

Lucas Dixon

2010-06-01

Full Text Available We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of half-edges (edges which are drawn with an unconnected end and enjoy rich compositional principles by connecting graphs along these half-edges. In particular, this allows equations and rewrite rules to be specified between graphs. Particular computational models can then be encoded as an axiomatic set of such rules. Further rules can be derived graphically and rewriting can be used to simulate the dynamics of a computational system, e.g. evaluating a program on an input. Examples of models which can be formalised in this way include traditional electronic circuits as well as recent categorical accounts of quantum information.

Properly colored connectivity of graphs

CERN Document Server

Li, Xueliang; Qin, Zhongmei

2018-01-01

A comprehensive survey of proper connection of graphs is discussed in this book with real world applications in computer science and network security. Beginning with a brief introduction, comprising relevant definitions and preliminary results, this book moves on to consider a variety of properties of graphs that imply bounds on the proper connection number. Detailed proofs of significant advancements toward open problems and conjectures are presented with complete references. Researchers and graduate students with an interest in graph connectivity and colorings will find this book useful as it builds upon fundamental definitions towards modern innovations, strategies, and techniques. The detailed presentation lends to use as an introduction to proper connection of graphs for new and advanced researchers, a solid book for a graduate level topics course, or as a reference for those interested in expanding and further developing research in the area.

Inferring ontology graph structures using OWL reasoning

KAUST Repository

Rodriguez-Garcia, Miguel Angel

2018-01-05

Ontologies are representations of a conceptualization of a domain. Traditionally, ontologies in biology were represented as directed acyclic graphs (DAG) which represent the backbone taxonomy and additional relations between classes. These graphs are widely exploited for data analysis in the form of ontology enrichment or computation of semantic similarity. More recently, ontologies are developed in a formal language such as the Web Ontology Language (OWL) and consist of a set of axioms through which classes are defined or constrained. While the taxonomy of an ontology can be inferred directly from the axioms of an ontology as one of the standard OWL reasoning tasks, creating general graph structures from OWL ontologies that exploit the ontologies\\' semantic content remains a challenge.We developed a method to transform ontologies into graphs using an automated reasoner while taking into account all relations between classes. Searching for (existential) patterns in the deductive closure of ontologies, we can identify relations between classes that are implied but not asserted and generate graph structures that encode for a large part of the ontologies\\' semantic content. We demonstrate the advantages of our method by applying it to inference of protein-protein interactions through semantic similarity over the Gene Ontology and demonstrate that performance is increased when graph structures are inferred using deductive inference according to our method. Our software and experiment results are available at http://github.com/bio-ontology-research-group/Onto2Graph .Onto2Graph is a method to generate graph structures from OWL ontologies using automated reasoning. The resulting graphs can be used for improved ontology visualization and ontology-based data analysis.

Inferring ontology graph structures using OWL reasoning.

Science.gov (United States)

Rodríguez-García, Miguel Ángel; Hoehndorf, Robert

2018-01-05

Ontologies are representations of a conceptualization of a domain. Traditionally, ontologies in biology were represented as directed acyclic graphs (DAG) which represent the backbone taxonomy and additional relations between classes. These graphs are widely exploited for data analysis in the form of ontology enrichment or computation of semantic similarity. More recently, ontologies are developed in a formal language such as the Web Ontology Language (OWL) and consist of a set of axioms through which classes are defined or constrained. While the taxonomy of an ontology can be inferred directly from the axioms of an ontology as one of the standard OWL reasoning tasks, creating general graph structures from OWL ontologies that exploit the ontologies' semantic content remains a challenge. We developed a method to transform ontologies into graphs using an automated reasoner while taking into account all relations between classes. Searching for (existential) patterns in the deductive closure of ontologies, we can identify relations between classes that are implied but not asserted and generate graph structures that encode for a large part of the ontologies' semantic content. We demonstrate the advantages of our method by applying it to inference of protein-protein interactions through semantic similarity over the Gene Ontology and demonstrate that performance is increased when graph structures are inferred using deductive inference according to our method. Our software and experiment results are available at http://github.com/bio-ontology-research-group/Onto2Graph . Onto2Graph is a method to generate graph structures from OWL ontologies using automated reasoning. The resulting graphs can be used for improved ontology visualization and ontology-based data analysis.

Optical generation of matter qubit graph states

International Nuclear Information System (INIS)

Benjamin, S C; Eisert, J; Stace, T M

2005-01-01

We present a scheme for rapidly entangling matter qubits in order to create graph states for one-way quantum computing. The qubits can be simple three-level systems in separate cavities. Coupling involves only local fields and a static (unswitched) linear optics network. Fusion of graph-state sections occurs with, in principle, zero probability of damaging the nascent graph state. We avoid the finite thresholds of other schemes by operating on two entangled pairs, so that each generates exactly one photon. We do not require the relatively slow single qubit local flips to be applied during the growth phase: growth of the graph state can then become a purely optical process. The scheme naturally generates graph states with vertices of high degree and so is easily able to construct minimal graph states, with consequent resource savings. The most efficient approach will be to create new graph-state edges even as qubits elsewhere are measured, in a 'just in time' approach. An error analysis indicates that the scheme is relatively robust against imperfections in the apparatus

XML Graphs in Program Analysis

DEFF Research Database (Denmark)

Møller, Anders; Schwartzbach, Michael I.

2011-01-01

of XML graphs against different XML schema languages, and provide a software package that enables others to make use of these ideas. We also survey the use of XML graphs for program analysis with four very different languages: XACT (XML in Java), Java Servlets (Web application programming), XSugar......XML graphs have shown to be a simple and effective formalism for representing sets of XML documents in program analysis. It has evolved through a six year period with variants tailored for a range of applications. We present a unified definition, outline the key properties including validation...

Graphs with Eulerian unit spheres

OpenAIRE

Knill, Oliver

2015-01-01

d-spheres in graph theory are inductively defined as graphs for which all unit spheres S(x) are (d-1)-spheres and that the removal of one vertex renders the graph contractible. Eulerian d-spheres are geometric d-spheres which are d+1 colorable. We prove here that G is an Eulerian sphere if and only if the degrees of all the (d-2)-dimensional sub-simplices in G are even. This generalizes a Kempe-Heawood result for d=2 and is work related to the conjecture that all d-spheres have chromatic numb...

The Container Problem in Bubble-Sort Graphs

Science.gov (United States)

Suzuki, Yasuto; Kaneko, Keiichi

Bubble-sort graphs are variants of Cayley graphs. A bubble-sort graph is suitable as a topology for massively parallel systems because of its simple and regular structure. Therefore, in this study, we focus on n-bubble-sort graphs and propose an algorithm to obtain n-1 disjoint paths between two arbitrary nodes in time bounded by a polynomial in n, the degree of the graph plus one. We estimate the time complexity of the algorithm and the sum of the path lengths after proving the correctness of the algorithm. In addition, we report the results of computer experiments evaluating the average performance of the algorithm.

Multiple graph regularized nonnegative matrix factorization

KAUST Repository

Wang, Jim Jing-Yan

2013-10-01

Non-negative matrix factorization (NMF) has been widely used as a data representation method based on components. To overcome the disadvantage of NMF in failing to consider the manifold structure of a data set, graph regularized NMF (GrNMF) has been proposed by Cai et al. by constructing an affinity graph and searching for a matrix factorization that respects graph structure. Selecting a graph model and its corresponding parameters is critical for this strategy. This process is usually carried out by cross-validation or discrete grid search, which are time consuming and prone to overfitting. In this paper, we propose a GrNMF, called MultiGrNMF, in which the intrinsic manifold is approximated by a linear combination of several graphs with different models and parameters inspired by ensemble manifold regularization. Factorization metrics and linear combination coefficients of graphs are determined simultaneously within a unified object function. They are alternately optimized in an iterative algorithm, thus resulting in a novel data representation algorithm. Extensive experiments on a protein subcellular localization task and an Alzheimer\\'s disease diagnosis task demonstrate the effectiveness of the proposed algorithm. © 2013 Elsevier Ltd. All rights reserved.

Graph Sampling for Covariance Estimation

KAUST Repository

Chepuri, Sundeep Prabhakar; Leus, Geert

2017-01-01

specialize for undirected circulant graphs in that the graph nodes leading to the best compression rates are given by the so-called minimal sparse rulers. A near-optimal greedy algorithm is developed to design the subsampling scheme for the non

Visual texture perception via graph-based semi-supervised learning

Science.gov (United States)

Zhang, Qin; Dong, Junyu; Zhong, Guoqiang

2018-04-01

Perceptual features, for example direction, contrast and repetitiveness, are important visual factors for human to perceive a texture. However, it needs to perform psychophysical experiment to quantify these perceptual features' scale, which requires a large amount of human labor and time. This paper focuses on the task of obtaining perceptual features' scale of textures by small number of textures with perceptual scales through a rating psychophysical experiment (what we call labeled textures) and a mass of unlabeled textures. This is the scenario that the semi-supervised learning is naturally suitable for. This is meaningful for texture perception research, and really helpful for the perceptual texture database expansion. A graph-based semi-supervised learning method called random multi-graphs, RMG for short, is proposed to deal with this task. We evaluate different kinds of features including LBP, Gabor, and a kind of unsupervised deep features extracted by a PCA-based deep network. The experimental results show that our method can achieve satisfactory effects no matter what kind of texture features are used.

Distribution of sizes of erased loops for loop-erased random walks

OpenAIRE

Dhar, Deepak; Dhar, Abhishek

1997-01-01

We study the distribution of sizes of erased loops for loop-erased random walks on regular and fractal lattices. We show that for arbitrary graphs the probability $P(l)$ of generating a loop of perimeter $l$ is expressible in terms of the probability $P_{st}(l)$ of forming a loop of perimeter $l$ when a bond is added to a random spanning tree on the same graph by the simple relation $P(l)=P_{st}(l)/l$. On $d$-dimensional hypercubical lattices, $P(l)$ varies as $l^{-\\sigma}$ for large $l$, whe...

The Quantitative Resolution of a Mixture of Group II Metal Ions by Thermometric Titration with EDTA. An Analytical Chemistry Experiment.

Science.gov (United States)

Smith, Robert L.; Popham, Ronald E.

1983-01-01

Presents an experiment in thermometric titration used in an analytic chemistry-chemical instrumentation course, consisting of two titrations, one a mixture of calcium and magnesium, the other of calcium, magnesium, and barium ions. Provides equipment and solutions list/specifications, graphs, and discussion of results. (JM)

Particle transport in breathing quantum graph

International Nuclear Information System (INIS)

Matrasulov, D.U.; Yusupov, J.R.; Sabirov, K.K.; Sobirov, Z.A.

2012-01-01

Full text: Particle transport in nanoscale networks and discrete structures is of fundamental and practical importance. Usually such systems are modeled by so-called quantum graphs, the systems attracting much attention in physics and mathematics during past two decades [1-5]. During last two decades quantum graphs found numerous applications in modeling different discrete structures and networks in nanoscale and mesoscopic physics (e.g., see reviews [1-3]). Despite considerable progress made in the study of particle dynamics most of the problems deal with unperturbed case and the case of time-dependent perturbation has not yet be explored. In this work we treat particle dynamics for quantum star graph with time-dependent bonds. In particular, we consider harmonically breathing quantum star graphs, the cases of monotonically contracting and expanding graphs. The latter can be solved exactly analytically. Edge boundaries are considered to be time-dependent, while branching point is assumed to be fixed. Quantum dynamics of a particle in such graphs is studied by solving Schrodinger equation with time-dependent boundary conditions given on a star graph. Time-dependence of the average kinetic energy is analyzed. Space-time evolution of the Gaussian wave packet is treated for harmonically breathing star graph. It is found that for certain frequencies energy is a periodic function of time, while for others it can be non-monotonically growing function of time. Such a feature can be caused by possible synchronization of the particles motion and the motions of the moving edges of graph bonds. (authors) References: [1] Tsampikos Kottos and Uzy Smilansky, Ann. Phys., 76, 274 (1999). [2] Sven Gnutzmann and Uzy Smilansky, Adv. Phys. 55, 527 (2006). [3] S. GnutzmannJ.P. Keating, F. Piotet, Ann. Phys., 325, 2595 (2010). [4] P.Exner, P.Seba, P.Stovicek, J. Phys. A: Math. Gen. 21, 4009 (1988). [5] J. Boman, P. Kurasov, Adv. Appl. Math., 35, 58 (2005)

High-performance analysis of filtered semantic graphs

OpenAIRE

Buluç, A; Fox, A; Gilbert, JR; Kamil, S; Lugowski, A; Oliker, L; Williams, S

2012-01-01

High performance is a crucial consideration when executing a complex analytic query on a massive semantic graph. In a semantic graph, vertices and edges carry \\attributes" of various types. Analytic queries on semantic graphs typically depend on the values of these attributes; thus, the computation must either view the graph through a filter that passes only those individual vertices and edges of interest, or else must first materialize a subgraph or subgraphs consisting of only the vertices ...

Bond graph modeling of centrifugal compression systems

OpenAIRE

Uddin, Nur; Gravdahl, Jan Tommy

2015-01-01

A novel approach to model unsteady fluid dynamics in a compressor network by using a bond graph is presented. The model is intended in particular for compressor control system development. First, we develop a bond graph model of a single compression system. Bond graph modeling offers a different perspective to previous work by modeling the compression system based on energy flow instead of fluid dynamics. Analyzing the bond graph model explains the energy flow during compressor surge. Two pri...

On the local edge antimagicness of m-splitting graphs

Science.gov (United States)

Albirri, E. R.; Dafik; Slamin; Agustin, I. H.; Alfarisi, R.

2018-04-01

Let G be a connected and simple graph. A split graph is a graph derived by adding new vertex v‧ in every vertex v‧ such that v‧ adjacent to v in graph G. An m-splitting graph is a graph which has m v‧-vertices, denoted by mSpl(G). A local edge antimagic coloring in G = (V, E) graph is a bijection f:V (G)\\to \\{1,2,3,\\ldots,|V(G)|\\} in which for any two adjacent edges e 1 and e 2 satisfies w({e}1)\

Augmented marked graphs

CERN Document Server

Cheung, King Sing

2014-01-01

Petri nets are a formal and theoretically rich model for the modelling and analysis of systems. A subclass of Petri nets, augmented marked graphs possess a structure that is especially desirable for the modelling and analysis of systems with concurrent processes and shared resources.This monograph consists of three parts: Part I provides the conceptual background for readers who have no prior knowledge on Petri nets; Part II elaborates the theory of augmented marked graphs; finally, Part III discusses the application to system integration. The book is suitable as a first self-contained volume

Co-Roman domination in graphs

Indian Academy of Sciences (India)

1National Centre for Advanced Research in Discrete Mathematics ... 3Department of Computer Science, Ball State University, Muncie, IN, USA .... The corona of two disjoint graphs G1 and G2 is defined to be the graph G = G1 ◦ G2,.

Nested Dynamic Condition Response Graphs

DEFF Research Database (Denmark)

Hildebrandt, Thomas; Mukkamala, Raghava Rao; Slaats, Tijs

2012-01-01

We present an extension of the recently introduced declarative process model Dynamic Condition Response Graphs ( DCR Graphs) to allow nested subgraphs and a new milestone relation between events. The extension was developed during a case study carried out jointly with our industrial partner...

A cluster algorithm for graphs

NARCIS (Netherlands)

S. van Dongen

2000-01-01

textabstractA cluster algorithm for graphs called the emph{Markov Cluster algorithm (MCL~algorithm) is introduced. The algorithm provides basically an interface to an algebraic process defined on stochastic matrices, called the MCL~process. The graphs may be both weighted (with nonnegative weight)

Exploring biological network structure with clustered random networks

Directory of Open Access Journals (Sweden)

Bansal Shweta

2009-12-01

Full Text Available Abstract Background Complex biological systems are often modeled as networks of interacting units. Networks of biochemical interactions among proteins, epidemiological contacts among hosts, and trophic interactions in ecosystems, to name a few, have provided useful insights into the dynamical processes that shape and traverse these systems. The degrees of nodes (numbers of interactions and the extent of clustering (the tendency for a set of three nodes to be interconnected are two of many well-studied network properties that can fundamentally shape a system. Disentangling the interdependent effects of the various network properties, however, can be difficult. Simple network models can help us quantify the structure of empirical networked systems and understand the impact of various topological properties on dynamics. Results Here we develop and implement a new Markov chain simulation algorithm to generate simple, connected random graphs that have a specified degree sequence and level of clustering, but are random in all other respects. The implementation of the algorithm (ClustRNet: Clustered Random Networks provides the generation of random graphs optimized according to a local or global, and relative or absolute measure of clustering. We compare our algorithm to other similar methods and show that ours more successfully produces desired network characteristics. Finding appropriate null models is crucial in bioinformatics research, and is often difficult, particularly for biological networks. As we demonstrate, the networks generated by ClustRNet can serve as random controls when investigating the impacts of complex network features beyond the byproduct of degree and clustering in empirical networks. Conclusion ClustRNet generates ensembles of graphs of specified edge structure and clustering. These graphs allow for systematic study of the impacts of connectivity and redundancies on network function and dynamics. This process is a key step in

On the Recognition of Fuzzy Circular Interval Graphs

OpenAIRE

Oriolo, Gianpaolo; Pietropaoli, Ugo; Stauffer, Gautier

2011-01-01

Fuzzy circular interval graphs are a generalization of proper circular arc graphs and have been recently introduced by Chudnovsky and Seymour as a fundamental subclass of claw-free graphs. In this paper, we provide a polynomial-time algorithm for recognizing such graphs, and more importantly for building a suitable representation.

The Thickness of Amalgamations and Cartesian Product of Graphs

Directory of Open Access Journals (Sweden)

Yang Yan

2017-08-01

Full Text Available The thickness of a graph is the minimum number of planar spanning subgraphs into which the graph can be decomposed. It is a measurement of the closeness to the planarity of a graph, and it also has important applications to VLSI design, but it has been known for only few graphs. We obtain the thickness of vertex-amalgamation and bar-amalgamation of graphs, the lower and upper bounds for the thickness of edge-amalgamation and 2-vertex-amalgamation of graphs, respectively. We also study the thickness of Cartesian product of graphs, and by using operations on graphs, we derive the thickness of the Cartesian product Kn □ Pm for most values of m and n.

On The Roman Domination Stable Graphs

Directory of Open Access Journals (Sweden)

Hajian Majid

2017-11-01

Full Text Available A Roman dominating function (or just RDF on a graph G = (V,E is a function f : V → {0, 1, 2} satisfying the condition that every vertex u for which f(u = 0 is adjacent to at least one vertex v for which f(v = 2. The weight of an RDF f is the value f(V (G = Pu2V (G f(u. The Roman domination number of a graph G, denoted by R(G, is the minimum weight of a Roman dominating function on G. A graph G is Roman domination stable if the Roman domination number of G remains unchanged under removal of any vertex. In this paper we present upper bounds for the Roman domination number in the class of Roman domination stable graphs, improving bounds posed in [V. Samodivkin, Roman domination in graphs: the class RUV R, Discrete Math. Algorithms Appl. 8 (2016 1650049].

Disease management research using event graphs.

Science.gov (United States)

Allore, H G; Schruben, L W

2000-08-01

Event Graphs, conditional representations of stochastic relationships between discrete events, simulate disease dynamics. In this paper, we demonstrate how Event Graphs, at an appropriate abstraction level, also extend and organize scientific knowledge about diseases. They can identify promising treatment strategies and directions for further research and provide enough detail for testing combinations of new medicines and interventions. Event Graphs can be enriched to incorporate and validate data and test new theories to reflect an expanding dynamic scientific knowledge base and establish performance criteria for the economic viability of new treatments. To illustrate, an Event Graph is developed for mastitis, a costly dairy cattle disease, for which extensive scientific literature exists. With only a modest amount of imagination, the methodology presented here can be seen to apply modeling to any disease, human, plant, or animal. The Event Graph simulation presented here is currently being used in research and in a new veterinary epidemiology course. Copyright 2000 Academic Press.

Measuring Two-Event Structural Correlations on Graphs

Science.gov (United States)

2012-08-01

2012 to 00-00-2012 4. TITLE AND SUBTITLE Measuring Two-Event Structural Correlations on Graphs 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ...by event simulation on the DBLP graph. Then we examine the efficiency and scala - bility of the framework with a Twitter network. The third part of...correlation pattern mining for large graphs. In Proc. of the 8th Workshop on Mining and Learning with Graphs, pages 119–126, 2010. [23] T. Smith. A

Reconstructing Nearly Simple Polytopes from their Graph

OpenAIRE

Doolittle, Joseph

2017-01-01

We present a partial description of which polytopes are reconstructible from their graphs. This is an extension of work by Blind and Mani (1987) and Kalai (1988), which showed that simple polytopes can be reconstructed from their graphs. In particular, we introduce a notion of $h$-nearly simple and prove that 1-nearly simple and 2-nearly simple polytopes are reconstructible from their graphs. We also give an example of a 3-nearly simple polytope which is not reconstructible from its graph. Fu...