Normal Approximation in Large Network Models

We develop a methodology for proving central limit theorems in network 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 tends to infinity. In the presence of strategic interactions, network moments are generally complex functions of components, where a node's component consists of all alters to which it is directly or indirectly connected. We find that a modification of "exponential stabilization" conditions from the stochastic geometry literature provides a useful formulation of weak dependence for moments of this type. We establish a CLT for a network moments satisfying stabilization and provide a methodology for deriving primitive sufficient conditions for stabilization using results in branching process theory. We apply the methodology to static and dynamic models of network formation.