  We investigate the evidence/flexibility (i.e., "Occam") paradigm and
demonstrate the theoretical and empirical consistency of Bayesian evidence for
the task of determining an appropriate generative model for network data. This
model selection framework involves determining a collection of candidate
models, equipping each of these models' parameters with prior distributions
derived via the encompassing priors method, and computing or approximating each
models' evidence. We demonstrate how such a criterion may be used to select the
most suitable model among the Erd\"{o}s-R\'{e}nyi (ER) model, independent edge
(IE) model, and rank-1 stochastic blockmodel (SBM). The Erd\"{o}s-R\'{e}nyi may
be considered as being linearly nested within IE, a fact which permits
exponential family results. The rank-1 SBM is not so ideal, so we propose a
numerical method to approximate its evidence. We apply this paradigm to brain
connectome data. Future work necessitates deriving and equipping additional
candidate random graph models with appropriate priors so they may be included
in the paradigm.
