  We propose a general model that jointly characterizes degree heterogeneity
and homophily in weighted, undirected networks. We present a moment estimation
method using node degrees and homophily statistics. We establish consistency
and asymptotic normality of our estimator using novel analysis. We apply our
general framework to three applications, including both exponential family and
non-exponential family models. Comprehensive numerical studies and a data
example also demonstrate the usefulness of our method.
