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233,464
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
Densities of MinorClosed Graph Families
, 2010
"... We define the limiting density of a minorclosed family of simple graphs F to be the smallest number k such that every nvertex graph in F has at most kn(1+o(1)) edges, and we investigate the set of numbers that can be limiting densities. This set of numbers is countable, wellordered, and closed; i ..."
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We define the limiting density of a minorclosed family of simple graphs F to be the smallest number k such that every nvertex graph in F has at most kn(1+o(1)) edges, and we investigate the set of numbers that can be limiting densities. This set of numbers is countable, wellordered, and closed
Factor Graphs and the SumProduct Algorithm
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1998
"... A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple c ..."
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Cited by 1787 (72 self)
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A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple
On the growth rate of minorclosed classes of graphs
, 2007
"... A minorclosed class of graphs is a set of labelled graphs which is closed under isomorphism and under taking minors. For a minorclosed class G, we let gn be the number of graphs in G which have n vertices. A recent result of Norine et al. [12] shows that for all minorclosed class G, there is a co ..."
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Cited by 2 (0 self)
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A minorclosed class of graphs is a set of labelled graphs which is closed under isomorphism and under taking minors. For a minorclosed class G, we let gn be the number of graphs in G which have n vertices. A recent result of Norine et al. [12] shows that for all minorclosed class G, there is a
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.
Graphbased algorithms for Boolean function manipulation
 IEEE TRANSACTIONS ON COMPUTERS
, 1986
"... In this paper we present a new data structure for representing Boolean functions and an associated set of manipulation algorithms. Functions are represented by directed, acyclic graphs in a manner similar to the representations introduced by Lee [1] and Akers [2], but with further restrictions on th ..."
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Cited by 3499 (47 self)
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In this paper we present a new data structure for representing Boolean functions and an associated set of manipulation algorithms. Functions are represented by directed, acyclic graphs in a manner similar to the representations introduced by Lee [1] and Akers [2], but with further restrictions
The PASCAL Visual Object Classes (VOC) challenge
, 2009
"... ... is a benchmark in visual object category recognition and detection, providing the vision and machine learning communities with a standard dataset of images and annotation, and standard evaluation procedures. Organised annually from 2005 to present, the challenge and its associated dataset has be ..."
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Cited by 624 (20 self)
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become accepted as the benchmark for object detection. This paper describes the dataset and evaluation procedure. We review the stateoftheart in evaluated methods for both classification and detection, analyse whether the methods are statistically different, what they are learning from the images (e
A Separator Theorem for Planar Graphs
, 1977
"... Let G be any nvertex planar graph. We prove that the vertices of G can be partitioned into three sets A, B, C such that no edge joins a vertex in A with a vertex in B, neither A nor B contains more than 2n/3 vertices, and C contains no more than 2& & vertices. We exhibit an algorithm which ..."
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Cited by 465 (1 self)
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Let G be any nvertex planar graph. We prove that the vertices of G can be partitioned into three sets A, B, C such that no edge joins a vertex in A with a vertex in B, neither A nor B contains more than 2n/3 vertices, and C contains no more than 2& & vertices. We exhibit an algorithm which
Results 1  10
of
233,464