  Exponential-family random network (ERN) models specify a joint representation
of both the dyads of a network and nodal characteristics. This class of models
allow the nodal characteristics to be modelled as stochastic processes,
expanding the range and realism of exponential-family approaches to network
modelling. In this paper we develop a theory of inference for ERN models when
only part of the network is observed, as well as specific methodology for
missing data, including non-ignorable mechanisms for network-based sampling
designs and for latent class models. In particular, we consider data collected
via contact tracing, of considerable importance to infectious disease
epidemiology and public health.
