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Community structures detection in complex network is important forunderstanding not only the topological structures of the network, but also thefunctions of it. Stochastic block model and nonnegative matrix factorizationare two widely used methods for community detection, which are proposed fromdifferent perspectives. In this paper, the relations between them are studied.The logarithm of likelihood function for stochastic block model can bereformulated under the framework of nonnegative matrix factorization. Besidesthe model equivalence, the algorithms employed by the two methods aredifferent. Preliminary numerical experiments are carried out to compare thebehaviors of the algorithms.

On Equivalence of Likelihood Maximization of Stochastic Block Model and Constrained Nonnegative Matrix Factorization