Normal Approximation in Large Network Models

Abstract: We prove a central limit theorem for network formation models with strategic interactions and homophilous agents. Since data often consists of observations on a single large network, we consider an asymptotic framework in which the network size diverges. We argue that a modification of ``stabilization'' conditions from the literature on geometric graphs provides a useful high-level formulation of weak dependence, which we utilize to establish an abstract central limit theorem. In the context of strategic network formation, we derive primitive conditions for stabilization using results in branching process theory. We outline a methodology for deriving primitive conditions that can be applied more broadly to other large network models with strategic interactions. Finally, we discuss practical inference procedures justified by our results.