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