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The community structure in complex networks as a typical meso-scale structure has received considerable attention; however, the other type of meso-scale structure—the core-periphery (abbreviated as CP) structure—has received much less attention than it deserves, even though the CP structure has been extensively observed in many social and biological systems. Recently, some researchers have begun to pay attention to this problem and designed some algorithms to detect the CP structure. Nevertheless, most of them aimed at detecting a single CP structure but cannot detect multiple pairs of CP structures. In addition, the two meso-scale structures are separately studied previously. In this work, we propose a simple and effective algorithm which can not only detect single as well as multiple pairs of CP structures, but also can simultaneously detect the CP structure and community structure in complex networks …