We explore the asymptotic properties of strategic models of network formation in very large populations. Specifically, we focus on (undirected) exponential random graph models. We want to recover a set of parameters from the individuals' utility functions using the observation of a single, but large, social network. We show that, under some conditions, a simple logit-based estimator is coherent, consistent and asymptotically normally distributed under a weak version of homophily. The approach is compelling as the computing time is minimal and the estimator can be easily implemented using pre-programmed estimators available in most statistical packages. We provide an application of our method using the Add Health database.