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Kronecker Graphs: An Approach to Modeling Networks (2010)
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| Venue: | JOURNAL OF MACHINE LEARNING RESEARCH 11 (2010) 985-1042 |
| Citations: | 123 - 3 self |
BibTeX
@MISC{Leskovec10kroneckergraphs:,
author = {Jure Leskovec and Deepayan Chakrabarti and Jon Kleinberg and Christos Faloutsos and Zoubin Ghahramani},
title = { Kronecker Graphs: An Approach to Modeling Networks},
year = {2010}
}
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Abstract
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 out-degree distribution, heavy tails for the eigenvalues and eigenvectors, small diameters, and densification and shrinking diameters over time. Current network models and generators either fail to match several of the above properties, are complicated to analyze mathematically, or both. Here we propose a generative model for networks that is both mathematically tractable and can generate networks that have all the above mentioned structural properties. Our main idea here is to use a non-standard matrix operation, the Kronecker product, to generate graphs which we refer to as “Kronecker graphs”. First, we show that Kronecker graphs naturally obey common network properties. In fact, we rigorously prove that they do so. We also provide empirical evidence showing that Kronecker graphs can effectively model the structure of real networks. We then present KRONFIT, a fast and scalable algorithm for fitting the Kronecker graph generation model to large real networks. A naive approach to fitting would take super-exponential
Keyphrases
kronecker graph modeling network heavy tail real network naive approach generative model large real network structural property non-standard matrix operation network property out-degree distribution empirical evidence scalable algorithm surprising property current network model rigorous analysis long list main idea realistic network kronecker graph generation model present kronfit tractable model kronecker product small diameter obey common network property
