Before revision:  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. The result delivers a square root n rate of convergence and a closed-form expression for the asymptotic variance. Then using techniques in branching process theory, we derive primitive conditions for stabilization in the following applications: static and dynamic models of strategic network formation , network regressions, and treatment effects with network spillovers.
After revision:  We first establish a general central limit theorem under high-level `stabilization' conditions that provide a useful formulation of weak dependence for moments of this type. Our first contribution is to prove a CLT for a large class of network moments satisfying stabilization and a moment condition. Our second contribution is a methodology for deriving primitive sufficient conditions for stabilization in the following applications: static and dynamic models of strategic network formation , network regressions, and treatment effects with network spillovers.