Core-periphery structure and community structure are two typical meso-scale structures in complex networks. Though the community detection has been extensively investigated from different perspectives, the definition and the detection of core-periphery structure have not received much attention. Furthermore, the detection problems of the core-periphery and community structure were separately investigated. In this paper, we develop a unified framework to simultaneously detect core-periphery structure and community structure in complex networks. Moreover, there are several extra advantages of our algorithm: our method can detect not only single but also multiple pairs of core-periphery structures; the overlapping nodes belonging to different communities can be identified; different scales of core-periphery structures can be detected by adjusting the size of core. The good performance of the method has been validated on synthetic and real complex networks. So we provide a basic framework to detect the two typical meso-scale structures: core-periphery structure and community structure.
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