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We investigate the evidence/flexibility (i.e., "Occam") paradigm anddemonstrate the theoretical and empirical consistency of Bayesian evidence forthe task of determining an appropriate generative model for network data. Thismodel selection framework involves determining a collection of candidatemodels, equipping each of these models' parameters with prior distributionsderived via the encompassing priors method, and computing or approximating eachmodels' evidence. We demonstrate how such a criterion may be used to select themost suitable model among the Erd\"{o}s-R\'{e}nyi (ER) model, independent edge(IE) model, and a special one-parameter low-rank stochastic blockmodel (SBM)with known memberships. The Erd\"{o}s-R\'{e}nyi may be considered as beinglinearly nested within IE, a fact which permits exponential family results. Theuniparametric SBM is not so ideal, so we propose a numerical method toapproximate the evidence. We apply this paradigm to brain connectome data.Future work necessitates deriving and equipping additional candidate randomgraph models with appropriate priors so they may be included in the paradigm.

Occam Factor for Random Graphs: Erd\"{o}s-R\'{e}nyi, Independent Edge, and a Uniparametric Stochastic Blockmodel