  We show posterior convergence for the community structure in the planted
bi-section model, for several interesting priors. Examples include where the
label on each vertex is iid Bernoulli distributed, with some parameter
$r\in(0,1)$. The parameter $r$ may be fixed, or equipped with a beta
distribution. We do not have constraints on the class sizes, which might be as
small as zero, or include all vertices, and everything in between. This enables
us to test between a uniform (Erd\"os-R\'enyi) random graph with no
distinguishable community or the planted bi-section model. The exact bounds for
posterior convergence enable us to convert credible sets into confidence sets.
Symmetric testing with posterior odds is shown to be consistent.
