On Equivalence of Likelihood Maximization of Stochastic Block Model and   Constrained Nonnegative Matrix Factorization
  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. 
Zhong-Yuan Zhang and Yujie Gai and Yu-Fei Wang and Hui-Min Cheng and   Xin Liu
cs.SI