  Stochastic Block Models (SBMs) are a fundamental tool for community detection
in network analysis. But little theoretical work exists on the statistical
performance of Bayesian SBMs, especially when the community count is unknown.
This paper studies a special class of SBMs whose community-wise connectivity
probability matrix is diagonally dominant, i.e., members of the same community
are more likely to connect with one another than with members from other
communities. The diagonal dominance constraint is embedded within an otherwise
weak prior, and, under mild regularity conditions, the resulting posterior
distribution is shown to concentrate on the true community count and membership
allocation as the network size grows to infinity. A reversible-jump Markov
Chain Monte Carlo posterior computation strategy is developed by adapting the
allocation sampler of Mcdaid et al (2013). Finite sample properties are
examined via simulation studies in which the proposed method offers competitive
estimation accuracy relative to existing methods under a variety of challenging
scenarios.
