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Exponential-family random graph models (ERGMs) provide a principled way tomodel and simulate features common in human social networks, such aspropensities for homophily and friend-of-a-friend triad closure. We show that,without adjustment, ERGMs preserve density as network size increases. Densityinvariance is often not appropriate for social networks. We suggest a simplemodification based on an offset which instead preserves the mean degree andaccommodates changes in network composition asymptotically. We demonstrate thatthis approach allows ERGMs to be applied to the important situation ofegocentrically sampled data. We analyze data from the National Health andSocial Life Survey (NHSLS).

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