Uncovering overlapping community structures by the key bi-community and intimate degree in bipartite networks

• Introduce the key bi-communities, the free-nodes and the intimate degree IND.
• Propose the algorithm 1 and the algorithm 2 for detecting the community structures in the bipartite networks.
• Find overlapping vertices.
• Give excellent experimental results.

Although many successful algorithms have been designed to discover community structures in network, most of them are dedicated to disjoint and non-overlapping communities. Very few of them are intended to discover overlapping communities, particularly the detection of such communities have hardly been explored in the bipartite networks. In this paper, a novel algorithm is proposed to detect overlapping community structures in bipartite networks. After analyzing the topological properties in bipartite networks, the key bi-communities and free-nodes are introduced. Firstly, some key bi-communities and free-nodes are extracted from the original bipartite networks. Then the free-nodes are allocated into a certain key bi-community by some given rules. In addition, the proposed algorithm successfully finds overlapping vertices between communities. Experimental results using some real-world networks data show that the performance of the proposed algorithm is satisfactory.