  Exponential-family random graph models (ERGMs) provide a principled and
flexible way to model and simulate features common in social networks, such as
propensities for homophily, mutuality, and friend-of-a-friend triad closure,
through choice of model terms (sufficient statistics). However, those ERGMs
modeling the more complex features have, to date, been limited to binary data:
presence or absence of ties. Thus, analysis of valued networks, such as those
where counts, measurements, or ranks are observed, has necessitated
dichotomizing them, losing information and introducing biases.
  In this work, we generalize ERGMs to valued networks. Focusing on modeling
counts, we formulate an ERGM for networks whose ties are counts and discuss
issues that arise when moving beyond the binary case. We introduce model terms
that generalize and model common social network features for such data and
apply these methods to a network dataset whose values are counts of
interactions.
