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Multicuts in Unweighted Graphs and Digraphs with Bounded Degree and Bounded TreeWidth
, 1998
"... this paper. Also, we show that Directed Edge Multicut is NPhard in digraphs with treewidth one and maximum in and out degree three. Other hardness results indicate why we cannot eliminate any of the three restrictionsunweighted, bounded degree and bounded treewidthon the input graph and sti ..."
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Cited by 23 (0 self)
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this paper. Also, we show that Directed Edge Multicut is NPhard in digraphs with treewidth one and maximum in and out degree three. Other hardness results indicate why we cannot eliminate any of the three restrictionsunweighted, bounded degree and bounded treewidthon the input graph
Distance oracles for unweighted graphs: breaking the quadratic barrier with constant additive error
, 2008
"... ..."
Fast Edge Splitting and Edmonds’ Arborescence Construction for Unweighted Graphs
"... Given an unweighted undirected or directed graph with n vertices, m edges and edge connectivity c, we present a new deterministic algorithm for edge splitting. Our algorithm splitsoff any specified subset S of vertices satisfying standard conditions (even degree for the undirected case and indegre ..."
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Cited by 7 (0 self)
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Given an unweighted undirected or directed graph with n vertices, m edges and edge connectivity c, we present a new deterministic algorithm for edge splitting. Our algorithm splitsoff any specified subset S of vertices satisfying standard conditions (even degree for the undirected case and in
Approximate shortest paths avoiding a failed vertex : optimal data structures for unweighted graphs
"... Abstract. Let G = (V, E) be any undirected graph on V vertices and E edges. A path P between any two vertices u, v ∈ V is said to be tapproximate shortest path if its length is at most t times the length of the shortest path between u and v. We consider the problem of building a compact data struct ..."
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Cited by 6 (0 self)
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Abstract. Let G = (V, E) be any undirected graph on V vertices and E edges. A path P between any two vertices u, v ∈ V is said to be tapproximate shortest path if its length is at most t times the length of the shortest path between u and v. We consider the problem of building a compact data
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
A fast and high quality multilevel scheme for partitioning irregular graphs
 SIAM JOURNAL ON SCIENTIFIC COMPUTING
, 1998
"... Recently, a number of researchers have investigated a class of graph partitioning algorithms that reduce the size of the graph by collapsing vertices and edges, partition the smaller graph, and then uncoarsen it to construct a partition for the original graph [Bui and Jones, Proc. ..."
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Cited by 1173 (16 self)
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Recently, a number of researchers have investigated a class of graph partitioning algorithms that reduce the size of the graph by collapsing vertices and edges, partition the smaller graph, and then uncoarsen it to construct a partition for the original graph [Bui and Jones, Proc.
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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divisions of a network. Here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix, which plays a role in community detection similar to that played by the graph Laplacian in graph partitioning calculations. This result leads us to a
Results 11  20
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27,980