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Adjusting for Network Size and Composition Effects in Exponential Random Graph Models

Exponential family random graph models (ERGMs) provide a principled way to model and simulate features common in human social networks, such as propensities for homophily and friend-of-a-friend triad closure. We show that, by default, ERGMs preserve density as network size increases. This density invariance is not realistic for most social networks, and we suggest a simple modification based on an offset term which instead preserves the mean degree asymptotically and accommodates changes in network composition. We demonstrate this approach on an egocentrically sampled data set.