Tied Kronecker product graph models to capture variance in network populations

Much of the past work on mining and modeling networks has focused on understanding the observed properties of single example graphs. However, in many real-life applications it is important to characterize the structure of populations of graphs. In this work, we investigate the distributional properties of Kronecker product graph models (KPGMs) [1]. Specifically, we examine whether these models can represent the natural variability in graph properties observed across multiple networks and find surprisingly that they cannot. By considering KPGMs from a new viewpoint, we can show the reason for this lack of variance theoretically - which is primarily due to the generation of each edge independently from the others. Based on this understanding we propose a generalization of KPGMs that uses tied parameters to increase the variance of the model, while preserving the expectation. We then show experimentally, that our mixed-KPGM can adequately capture the natural variability across a population of networks.