  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.
