  Community structures detection in complex network is important for
understanding not only the topological structures of the network, but also the
functions of it. Stochastic block model and nonnegative matrix factorization
are two widely used methods for community detection, which are proposed from
different perspectives. In this paper, the relations between them are studied.
The logarithm of likelihood function for stochastic block model can be
reformulated under the framework of nonnegative matrix factorization. Besides
the model equivalence, the algorithms employed by the two methods are
different. Preliminary numerical experiments are carried out to compare the
behaviors of the algorithms.
