Kronecker Graphs: An Approach to Modeling Networks

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 provi...

• Type: Journal
• Year: 2010
• Where: JMLR
• Authors: Jure Leskovec, Deepayan Chakrabarti, Jon M. Kleinberg, Christos Faloutsos, Zoubin Ghahramani
• Keywords: JMLR 2010, Kronecker, Network Properties, Real Networks