Network Hypothesis Testing Using Mixed Kronecker Product Graph Models

The recent interest in networks-social, physical, communication, information, etc.-has fueled a great deal of research on the analysis and modeling of graphs. However, many of the analyses have focused on a single large network (e.g., a subnetwork sampled from Facebook). Although several studies have compared networks from different domains or samples, they largely focus on empirical exploration of network similarities rather than explicit tests of hypotheses. This is in part due to a lack of statistical methods to determine whether two large networks are likely to have been drawn from the same underlying graph distribution. Research on across-network hypothesis testing methods has been limited by (i) difficulties associated with obtaining a set of networks to reason about the underlying graph distribution, and (ii) limitations of current statistical models of graphs that make it difficult to represent variations across networks. In this paper, we exploit the recent development of mixed-Kronecker Product Graph Models, which accurately capture the natural variation in real world graphs, to develop a model-based approach for hypothesis testing in networks.