Before revision:  We then use an inductive "in-fill and out-expansion" algorithm to establish our main results, and consider extensions to more general settings that allow nonseparable dependence between homophily and degree heterogeneity  .
After revision:  We then use an inductive "in-fill and out-expansion" algorithm to establish our main results, and consider extensions to more general settings that allow nonseparable dependence between homophily and degree heterogeneity , as well as certain extents of network sparsity and weaker assumptions on the support of unobserved heterogeneity. As a byproduct, we also propose a concept called "modeling equivalence" as a refinement of "observational equivalence", and use it to provide a formal discussion about normalization, identification and their interplay with counterfactuals .