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Kronecker Graphs: An Approach to Modeling Networks
 JOURNAL OF MACHINE LEARNING RESEARCH 11 (2010) 9851042
, 2010
"... How can we generate realistic networks? In addition, how can we do so with a mathematically tractable model that allows for rigorous analysis of network properties? Real networks exhibit a long list of surprising properties: Heavy tails for the in and outdegree distribution, heavy tails for the ei ..."
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Cited by 123 (3 self)
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mathematically tractable and can generate networks that have all the above mentioned structural properties. Our main idea here is to use a nonstandard matrix operation, the Kronecker product, to generate graphs which we refer to as “Kronecker graphs”. First, we show that Kronecker graphs naturally obey common
Properties of Stochastic Kronecker Graph
, 2012
"... The stochastic Kronecker Graph model can generate large random graph that closely resembles many real world networks. For example, the output graph has a heavytailed degree distribution, has a (low) diameter that effectively remains constant over time and obeys the socalled densification power law ..."
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The stochastic Kronecker Graph model can generate large random graph that closely resembles many real world networks. For example, the output graph has a heavytailed degree distribution, has a (low) diameter that effectively remains constant over time and obeys the socalled densification power
Stochastic kronecker graphs
 Proceedings of the 5th Workshop on Algorithms and Models for the WebGraph
, 2007
"... A random graph model based on Kronecker products of probability matrices has been recently proposed as a generative model for largescale realworld networks such as the web. This model simultaneously captures several wellknown properties of realworld networks; in particular, it gives rise to a he ..."
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Cited by 27 (2 self)
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A random graph model based on Kronecker products of probability matrices has been recently proposed as a generative model for largescale realworld networks such as the web. This model simultaneously captures several wellknown properties of realworld networks; in particular, it gives rise to a
CONNECTIVITY AND GIANT COMPONENT OF STOCHASTIC KRONECKER GRAPHS
"... Abstract. Stochastic Kronecker graphs are a model for complex networks where each edge is present independently according the Kronecker (tensor) product of a fixed matrix P ∈ [0, 1]k×k. We develop a novel correspondence between the adjacencies in a general stochastic Kronecker graph and the action o ..."
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Cited by 1 (0 self)
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Abstract. Stochastic Kronecker graphs are a model for complex networks where each edge is present independently according the Kronecker (tensor) product of a fixed matrix P ∈ [0, 1]k×k. We develop a novel correspondence between the adjacencies in a general stochastic Kronecker graph and the action
Human Activities as Stochastic Kronecker Graphs
, 2012
"... A human activity can be viewed as a spacetime repetition of activity primitives. Both instances of the primitives, and their repetition are stochastic. They can be modeled by a generative modelgraph, where nodes correspond to the primitives, and the graph’s adjacency matrix encodes their affinit ..."
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Cited by 6 (0 self)
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successive Kronecker multiplication of the model’s affinity matrix. The resulting Kroneckerpower matrix is taken as a noisy permutation of the adjacency matrix of the video graph. The paper presents our: 1) modelgraph; 2) memory and timeefficient, weakly supervised learning of activity primitives
Generalizing Kronecker graphs in order to model searchable networks
 IN PROC. FORTYSEVENTH ANNUAL ALLERTON CONFERENCE
, 2009
"... This paper describes an extension to stochastic Kronecker graphs that provides the special structure required for searchability, by defining a “distance”dependent Kronecker operator. We show how this extension of Kronecker graphs can generate several existing social network models, such as the Watt ..."
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Cited by 2 (0 self)
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This paper describes an extension to stochastic Kronecker graphs that provides the special structure required for searchability, by defining a “distance”dependent Kronecker operator. We show how this extension of Kronecker graphs can generate several existing social network models
Distancedependent Kronecker Graphs for Modeling Social Networks
, 2009
"... This paper focuses on a generalization of stochastic Kronecker graphs, introducing a Kroneckerlike operator and defining a family of generator matrices H dependent on distances between nodes in a specified graph embedding. We prove that any latticebased network model with sufficiently small distan ..."
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Cited by 2 (1 self)
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This paper focuses on a generalization of stochastic Kronecker graphs, introducing a Kroneckerlike operator and defining a family of generator matrices H dependent on distances between nodes in a specified graph embedding. We prove that any latticebased network model with sufficiently small
Moment based estimation of stochastic Kronecker graph parameters
, 2008
"... Stochastic Kronecker graphs supply a parsimonious model for large sparse real world graphs. They can specify the distribution of a large random graph using only three or four parameters. Those parameters have however proved difficult to choose in specific applications. This article looks at method o ..."
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Stochastic Kronecker graphs supply a parsimonious model for large sparse real world graphs. They can specify the distribution of a large random graph using only three or four parameters. Those parameters have however proved difficult to choose in specific applications. This article looks at method
Moment based estimation of stochastic Kronecker graph parameters
, 2011
"... Stochastic Kronecker graphs supply a parsimonious model for large sparse real world graphs. They can specify the distribution of a large random graph using only three or four parameters. Those parameters have however proved difficult to choose in specific applications. This article looks at method o ..."
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Cited by 5 (0 self)
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Stochastic Kronecker graphs supply a parsimonious model for large sparse real world graphs. They can specify the distribution of a large random graph using only three or four parameters. Those parameters have however proved difficult to choose in specific applications. This article looks at method
Results 1  10
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