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Topological Properties of an Exponential Random Geometric Graph Process
"... Abstractâ€”In this paper we consider a onedimensional random geometric graph process with the internodal gaps evolving according to an exponential AR(1) process. The transition probability matrix and stationary distribution are derived for the Markov chains concerning connectivity and the number of ..."
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Abstractâ€”In this paper we consider a onedimensional random geometric graph process with the internodal gaps evolving according to an exponential AR(1) process. The transition probability matrix and stationary distribution are derived for the Markov chains concerning connectivity and the number
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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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
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 Framework for Dynamic Graph Drawing
 CONGRESSUS NUMERANTIUM
, 1992
"... Drawing graphs is an important problem that combines flavors of computational geometry and graph theory. Applications can be found in a variety of areas including circuit layout, network management, software engineering, and graphics. The main contributions of this paper can be summarized as follows ..."
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Cited by 627 (44 self)
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Drawing graphs is an important problem that combines flavors of computational geometry and graph theory. Applications can be found in a variety of areas including circuit layout, network management, software engineering, and graphics. The main contributions of this paper can be summarized
Measuring ISP Topologies with Rocketfuel
 In Proc. ACM SIGCOMM
, 2002
"... To date, realistic ISP topologies have not been accessible to the research community, leaving work that depends on topology on an uncertain footing. In this paper, we present new Internet mapping techniques that have enabled us to directly measure routerlevel ISP topologies. Our techniques reduce t ..."
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Cited by 838 (30 self)
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To date, realistic ISP topologies have not been accessible to the research community, leaving work that depends on topology on an uncertain footing. In this paper, we present new Internet mapping techniques that have enabled us to directly measure routerlevel ISP topologies. Our techniques reduce
A Critical Point For Random Graphs With A Given Degree Sequence
, 2000
"... Given a sequence of nonnegative real numbers 0 ; 1 ; : : : which sum to 1, we consider random graphs having approximately i n vertices of degree i. Essentially, we show that if P i(i \Gamma 2) i ? 0 then such graphs almost surely have a giant component, while if P i(i \Gamma 2) i ! 0 the ..."
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Cited by 511 (8 self)
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Given a sequence of nonnegative real numbers 0 ; 1 ; : : : which sum to 1, we consider random graphs having approximately i n vertices of degree i. Essentially, we show that if P i(i \Gamma 2) i ? 0 then such graphs almost surely have a giant component, while if P i(i \Gamma 2) i ! 0
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
Randomized Algorithms
, 1995
"... Randomized algorithms, once viewed as a tool in computational number theory, have by now found widespread application. Growth has been fueled by the two major benefits of randomization: simplicity and speed. For many applications a randomized algorithm is the fastest algorithm available, or the simp ..."
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Cited by 2210 (37 self)
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Randomized algorithms, once viewed as a tool in computational number theory, have by now found widespread application. Growth has been fueled by the two major benefits of randomization: simplicity and speed. For many applications a randomized algorithm is the fastest algorithm available
Results 1  10
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378,154