A Bootstrap-based Inference Framework for Testing Similarity of Paired Networks

We live in an interconnected world where network valued data arises in many domains, and, fittingly, statistical network analysis has emerged as an active area in the literature. However, the topic of inference in networks has received relatively less attention. In this work, we consider the paired network inference problem where one is given two networks on the same set of nodes, and the goal is to test whether the given networks are stochastically similar in terms of some notion of similarity. We develop a general inferential framework based on parametric bootstrap to address this problem. Under this setting, we address two specific and important problems: the equality problem, i.e., whether the two networks are generated from the same random graph model, and the scaling problem, i.e., whether the underlying probability matrices of the two random graph models are scaled versions of each other.