Random graphs, where the presence of connections between nodes are considered random variables, have wide applicability in the social sciences. Exponentialfamily Random Graph Models (ERGM) have shown themselves to be a useful class of models for representing complex social phenomena. We generalize ERGM by also modeling nodal attributes as random variates, thus creating a random model of the full network, which we call Exponential-family Random Network Models (ERNM). We demonstrate how this framework allows a new formulation for logistic regression in network data. We develop likelihood-based inference for the model in the case of a fully observed network and an MCMC algorithm to implement it.

We then develop a theory of inference for ERNM when only part of the network is observed, as well as specifc methodology for missing data, including nonignorable mechanisms for network-based sampling designs and for latent class models. We also consider contact tracing sampling designs which are of considerable importance to infectious disease epidemiology and public health. This culminates in a treatment of respondent driven sampling (RDS), which is a widely used link tracing design.