  The Degree Corrected Stochastic Block Model (DCSBM) was introduced by
\cite{karrer2011stochastic} as a generalization of the stochastic block model
in which vertices of the same community are allowed to have distinct degree
distributions. On the modelling side, this variability makes the DCSBM more
suitable for real life complex networks. On the statistical side, it is more
challenging due to the large number of parameters when dealing with community
detection. In this paper we prove that the penalized marginal likelihood
estimator is strongly consistent for the estimation of the number of
communities. We consider \emph{dense} or \emph{semi-sparse} random networks,
and our estimator is \emph{unbounded}, in the sense that the number of
communities $k$ considered can be as big as $n$, the number of nodes in the
network.
