  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.
