Multicore-periphery structure in networks

Many real-world networked systems exhibit a multicore-periphery structure, i.e., multiple cores, each of which contains densely connected elements, surrounded by sparsely connected elements that define the periphery. Identification of the multiple-periphery structure can provide a new handle on structures and functions of various complex networks, such as cognitive and biological networks, food webs, social networks, and communication and transportation networks. However, still no quantitative method exists to identify the multicore-periphery structure embedded in networks. Prior studies on core-periphery structure focused on either dichotomous or continuous division of a network into a single core and a periphery, whereas community detection algorithms did not discern the periphery from dense cohesive communities. Herein, we introduce a method to identify the optimal partition of a network into multiple dense cores and a loosely-connected periphery, and test the method on a well-known social network and the technology space network, which are best characterized by multiple-core structures. Our method gives precise and meaningful results. The analysis of multicore-periphery structure may advance our understandings of the structures and functions in diverse real-world networks.