Before revision:  The results hold under large-network asymptotics, enabling inference in the typical setting where the sample consists of a small set of large networks. We first establish a general central limit theorem under high-level `stabilization' conditions that provide a useful formulation of weak dependence , particularly in models with strategic interactions.
After revision:  The results hold under large-network asymptotics, enabling inference in the typical setting where the sample consists of a single large network. In the presence of strategic interactions, network moments are generally complex functions of network 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 , particularly in models with strategic interactions.