Fuzzy analysis for overlapping community structure of complex network

We consider the problem of fuzzy community detection in networks, which complements the concept of overlapping community structure. Using the optimization method to approximate network feature matrix is an important approach for conventional fuzzy community detection. In order to retain valuable physical meaning of the approximation, we discard redundant constraints in the process of approximation which is accordingly reduced to a problem of symmetrical non-negative matrix factorization (s-NMF). The resulting fuzzy metric, which is termed clique-node similarity degree (CNSD), is able to grasp very subtle topology information of the node´s neighborhood. Based on the CNSD, we introduce a new measure that is able to identify the key nodes that are critical to the connection of the adjacent communities. The technique is able to discover the fuzzy community structure of different real world networks with high confidence.