Core-periphery structure in networks (revisited)

Intermediate-scale (or 'meso-scale') structures in networks have received considerable attention, as the algorithmic detection of such structures makes it possible to discover network features that are not apparent either at the local scale of nodes and edges or at the global scale of summary statistics. Numerous types of meso-scale structures can occur in networks, but investigations of meso-scale network features have focused predominantly on the identification and study of community structure. In this paper, we develop a new method to investigate the meso-scale feature known as coreperiphery structure, which consists of an identification of a network's nodes into a densely connected core and a sparsely connected periphery. In contrast to traditional network communities, the nodes in a core are also reasonably well-connected to those in the periphery. Our new method of computing core-periphery structure can identify multiple cores in a network and takes different possible cores into account, thereby enabling a detailed description of core-periphery structure. We illustrate the differences between our method and existing methods for identifying which nodes belong to a core, and we use it to classify the most important nodes using examples of friendship, collaboration, transportation, and voting networks