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Community detection in graphs
, 2009
"... The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of th ..."
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Cited by 801 (1 self)
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The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices
Sum Edge Colorings of Multigraphs . . .
"... We consider the scheduling of biprocessor jobs under sum objective (BPSMS). Given a collection of unitlength jobs where each job requires the use of two processors, find a schedule such that no two jobs involving the same processor run concurrently. The objective is to minimize the sum of the compl ..."
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of the completion times of the jobs. Equivalently, we would like to find a sum edge coloring of a given multigraph, i.e. a partition of its edge set into matchings M1,..., Mt minimizing Pt i=1 iMi. This problem is APXhard, even in the case of bipartite graphs [Marx 2009]. This special case is closely related
EdgeColoring Bipartite Multigraphs in O(E log D) Time
, 1999
"... Let V , E, and D denote the cardinality of the vertex set, the cardinality of the edge set, and the maximum degree of a bipartite multigraph G. We show that a minimal edgecoloring of G can be computed in O(E log D) time. 1 Introduction The edgecoloring problem is to nd a minimal edgecoloring ..."
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Cited by 55 (0 self)
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Let V , E, and D denote the cardinality of the vertex set, the cardinality of the edge set, and the maximum degree of a bipartite multigraph G. We show that a minimal edgecoloring of G can be computed in O(E log D) time. 1 Introduction The edgecoloring problem is to nd a minimal edgecoloring
Finding community structure in networks using the eigenvectors of matrices
, 2006
"... We consider the problem of detecting communities or modules in networks, groups of vertices with a higherthanaverage density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as “modularity ” over possible div ..."
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Cited by 500 (0 self)
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number of possible algorithms for detecting community structure, as well as several other results, including a spectral measure of bipartite structure in networks and a new centrality measure that identifies those vertices that occupy central positions within the communities to which they belong
An open graph visualization system and its applications to software engineering
 SOFTWARE  PRACTICE AND EXPERIENCE
, 2000
"... We describe a package of practical tools and libraries for manipulating graphs and their drawings. Our design, which aimed at facilitating the combination of the package components with other tools, includes stream and event interfaces for graph operations, highquality static and dynamic layout alg ..."
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Cited by 452 (9 self)
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algorithms, and the ability to handle sizable graphs. We conclude with a description of the applications of this package to a variety of software engineering tools.
Approximating Maximum Edge Coloring in Multigraphs
 In APPROX, volume 2462 of LNCS
, 2002
"... We study the complexity of the following problem that we call Max edge tcoloring: given a multigraph G and a parameter t, color as many edges as possible using t colors, such that no two adjacent edges are colored with the same color. (Equivalently, find the largest edge induced subgraph of G that ..."
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Cited by 8 (0 self)
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We study the complexity of the following problem that we call Max edge tcoloring: given a multigraph G and a parameter t, color as many edges as possible using t colors, such that no two adjacent edges are colored with the same color. (Equivalently, find the largest edge induced subgraph of G
Edge Coloring Bipartite Graphs Efficiently
"... The chromatic index of a bipartite graph equals the maximal degree \Delta of its vertices. The straightforward way to compute the corresponding edge coloring using \Delta colors, requires O(\Delta 2 \Delta n 3=2 ) time. We will show that a simple divide & conquer algorithm only requires O(\ ..."
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The chromatic index of a bipartite graph equals the maximal degree \Delta of its vertices. The straightforward way to compute the corresponding edge coloring using \Delta colors, requires O(\Delta 2 \Delta n 3=2 ) time. We will show that a simple divide & conquer algorithm only requires O
Graphical models, exponential families, and variational inference
, 2008
"... The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fiel ..."
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Cited by 800 (26 self)
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likelihoods, marginal probabilities and most probable configurations. We describe how a wide varietyof algorithms — among them sumproduct, cluster variational methods, expectationpropagation, mean field methods, maxproduct and linear programming relaxation, as well as conic programming relaxations — can
On the Ramsey Numbers for Bipartite Multigraphs
, 2003
"... A coloring of a complete bipartite graph is shufflepreserved if it is the case that assigning a color c to edges (u,v) and (u′,v ′) enforces the same color assignment for edges (u,v ′) and (u′,v). (In words, the induced subgraph with respect to color c is complete.) In this paper, we investigate a ..."
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variant of the Ramsey problem for the class of complete bipartite multigraphs. (By a multigraph we mean a graph in which multiple edges, but no loops, are allowed.) Unlike the conventional mcoloring scheme in Ramsey theory which imposes a constraint (i.e., m) on the total number of colors allowed in a
Results 1  10
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