  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. The binary or nonbinary network edges are
simultaneously considered. We establish a unified theoretical framework under
which the consistency of the moment estimator holds as the size of networks
goes to infinity. We also derive the asymptotic representation of the moment
estimator that can be used to characterize its limiting distribution. The
asymptotic representation of the moment estimator of the homophily parameter
contains a bias term. Two applications are provided to illustrate the
theoretical result. Numerical studies and a real data analysis demonstrate our
theoretical findings.
