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This article introduces a new class of models for multiple networks. The coreidea is to parametrize a distribution on labelled graphs in terms of aFr\'{e}chet mean graph (which depends on a user-specified choice of metric orgraph distance) and a parameter that controls the concentration of thisdistribution about its mean. Entropy is the natural parameter for such control,varying from a point mass concentrated on the Fr\'{e}chet mean itself to auniform distribution over all graphs on a given vertex set. We provide ahierarchical Bayesian approach for exploiting this construction, along withstraightforward strategies for sampling from the resultant posteriordistribution. We conclude by demonstrating the efficacy of our approach viasimulation studies and two multiple-network data analysis examples: one drawnfrom systems biology and the other from neuroscience.

Modeling Network Populations via Graph Distances