We prove a central limit theorem for network moments in a model of network formation 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 "exponential stabilization" conditions from the literature on geometric graphs provides a useful high-level formulation of weak dependence, which we use to establish an abstract central limit theorem. We then derive primitive conditions for stabilization using results in branching process theory. We discuss practical inference procedures justified by our results and outline a methodology for deriving primitive conditions that can be applied more broadly to other large network models with strategic interactions.

翻译：我们证明了一个在具有策略互动和同质性主体的网络形成模型中的网络矩中心极限定理。由于数据通常仅包含对单个大型网络的观测，我们考虑网络规模发散的渐进框架。我们认为，对几何图文献中"指数稳定性"条件的修改，为弱依赖性提供了一个有用的高层次表述，并利用此建立了抽象的中心极限定理。随后，我们利用分支过程理论的结果推导出稳定性的原始条件。我们讨论了由我们的结果所证实的实用推断程序，并概述了一种可更广泛地应用于其他具有策略互动的大型网络模型、用以推导原始条件的方法。