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A Bayesian approach to conduct network model selection is presented for ageneral class of network models referred to as the congruence class models(CCMs). CCMs form a broad class that includes as special cases several commonnetwork models, such as the Erd\H{o}s-R\'{e}nyi-Gilbert model, stochastic blockmodel and many exponential random graph models. Due to the range of models ableto be specified as a CCM, investigators are better able to select a modelconsistent with generative mechanisms associated with the observed networkcompared to current approaches. In addition, the approach allows forincorporation of prior information. We utilize the proposed Bayesian networkmodel selection approach for CCMs to investigate several mechanisms that may beresponsible for the structure of patient-sharing networks, which are associatedwith the cost and quality of medical care. We found evidence in support ofheterogeneity in sociality but not selective mixing by provider type nordegree.

Investigation of Patient-sharing Networks Using a Bayesian Network Model Selection Approach for Congruence Class Models