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Abstract Non-negative Matrix Factorization technique has attracted many interests in overlapping community detection due to its performance and interpretability. However, when adapted to discover community structure the intrinsic geometric information of the network graph is seldom considered. In view of this, we proposed a novel NMF based algorithm called Graph regularized nonnegative matrix tri-factorization (GNMTF) model, which incorporates the intrinsic geometrical properties of the network graph by manifold regularization. Moreover, by using three factor matrices we can not only explicitly obtain the community membership of each node but also learn the interaction among different communities. The experimental results on two well-known real world networks and a benchmark network demonstrate the effectiveness of the algorithm over the representative non-negative matrix factorization based method. Highlights • By consideration of the low-dimensional manifold it could achieve better results. • The number of communities can be determined by analysis of the spectrum properties. • It merges advantages of fuzzy and non-fuzzy overlapping community detection methods. [ABSTRACT FROM AUTHOR]