  The stochastic block model (SBM) is a probabilistic model de- signed to
describe heterogeneous directed and undirected graphs. In this paper, we
address the asymptotic inference on SBM by use of maximum- likelihood and
variational approaches. The identi ability of SBM is proved, while asymptotic
properties of maximum-likelihood and variational esti- mators are provided. In
particular, the consistency of these estimators is settled, which is, to the
best of our knowledge, the rst result of this type for variational estimators
with random graphs.
