Community structure has been recognized as an important statistical feature of networked systems over the past decade. A lot of work has been done to discover isolated communities from a network, and the focus was on developing of algorithms with high quality and good performance. However, there is less work done on the discovery of overlapping community structure, even though it could better capture the nature of network in some real-world applications. For example, people are always provided with varying characteristics and interests, and are able to join very different communities in their social network. In this context, we present a novel overlapping community structures detecting algorithm which first finds the seed sets by the spectral partition and then extends them with a special random walks technique. At every expansion step, the modularity function Q is chosen to measure the expansion structures. The function has become one of the popular standards in community detecting and is defined in Newman and Girvan (Phys. Rev. 69:026113, 2004 ). We also give a theoretic analysis to the whole expansion process and prove that our algorithm gets the best community structures greedily. Extensive experiments are conducted in real-world networks with various sizes. The results show that overlapping is important to find the complete community structures and our method outperforms the C -means in quality.
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