# Normal Approximation in Large Network Models

## TL;DR

This paper establishes a central limit theorem for large network models with strategic interactions, enabling statistical inference on single large networks by leveraging stabilization conditions and branching process theory.

## Contribution

It introduces a novel stabilization framework for network models with strategic interactions, providing primitive conditions for asymptotic normality.

## Key findings

- Proves a central limit theorem for large network models with homophily and strategic interactions.
- Provides primitive conditions for stabilization based on branching process theory.
- Discusses practical inference procedures justified by the theoretical results.

## 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. Using results in branching process theory, we derive interpretable primitive conditions for stabilization. The main conditions restrict the strength of strategic interactions and equilibrium selection mechanism. We discuss practical inference procedures justified by our results.