  Posterior distributions for community structure in sparse planted bi-section
models are shown to achieve exact (resp. almost-exact) recovery, with sharp
bounds for the sparsity regimes where edge probabilities decrease as
$O(\log(n)/n)$ (resp. $O(1/n)$). Assuming posterior recovery, one may interpret
credible sets (resp. enlarged credible sets) as asymptotically consistent
confidence sets; the diameters of those credible sets are controlled by the
rate of posterior concentration. If credible levels are chosen to grow to one
quickly enough, corresponding credible sets can be interpreted as frequentist
confidence sets without conditions on posterior concentration. In the regimes
with $O(1/n)$ edge sparsity, or when within-community and between-community
edge probabilities are very close, credible sets may be enlarged to achieve
frequentist asymptotic coverage, also without conditions on posterior
concentration.
