Social network data, consisting of relationships between actors and sometimes represented by graphs, have been widely modeled by Exponential-Family Random Graph Models (ERGMs). An important practical stumbling block for modeling observed data by ERGMs is the so-called near-degeneracy problem: ERGMs tend to place most probability mass on a small number of graphs; the graphs with non-negligible probability mass do not resemble observed data; and ERGMs are unstable in the sense that small changes in parameter values are associated with large changes in the probability mass function. The near-degeneracy problem of ERGMs has important consequences for simulating data from ERGMs and inferring from observed data to ERGMs. Some proposed solutions (e.g.\ curved exponential-family models) have alleviated, but not solved, the near-degeneracy problem. We propose hierarchical, non-parametric Bayesian extensions of ERGMs with a view to solving the near-degeneracy problem. The proposed modeling framework is simple, general, and has an appealing interpretation in social science terms. We demonstrate its usefulness by applying it to empirical social networks.

# Toward a Solution of the Near-Degeneracy Problem of Exponential-Family Random Graph Models

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