We propose a unied framework for studying both latent and
stochastic block models, which are used to cluster simultaneously rows
and columns of a data matrix. In this new framework, we study the
behaviour of the groups posterior distribution, given the data. We
characterize whether it is possible to asymptotically recover the
actual groups on the rows and columns of the matrix. In other words,
we establish sucient conditions for the groups posterior distribution
to converge (as the size of the data increases) to a Dirac mass
located at the actual (random) groups conguration. In particular, we
highlight some cases where the model assumes symmetries in the matrix
of connection probabilities that prevents from a correct recovering of
the groups. We also discuss the validity of these results when the
proportion of non-null entries in the data matrix converges to zero.