Undirected network models with degree heterogeneity and homophily

The degree heterogeneity and homophily are two typical features in network data. In this paper, we formulate a general model for undirected networks with these two features and present the moment estimation for inferring the degree and homophily parameters. Our model only specifies a marginal distribution on each edge in weighted or unweighted graphs and admits the non-independent dyad structures unlike previous works that assume independent dyads. We establish a unified theoretical framework under which the consistency of the moment estimator hold as the size of networks goes to infinity. We also derive its asymptotic representation that can be used to characterize its limiting distribution. The asymptotic representation of the estimator of the homophily parameter contains a bias term. Accurate inference necessitates bias-correction.Several applications are provided to illustrate the unified theoretical result.

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