Detection of core-periphery structure in networks based on 3-tuple motifs

Detecting mesoscale structure, such as community structure, is of vital importance for analyzing complex networks. Recently, a new mesoscale structure, core-periphery (CP) structure, has been identified in many real-world systems. In this paper, we propose an effective algorithm for detecting CP structure based on a 3-tuple motif. In this algorithm, we first define a 3-tuple motif in terms of the patterns of edges as well as the property of nodes, and then a motif adjacency matrix is constructed based on the 3-tuple motif. Finally, the problem is converted to find a cluster that minimizes the smallest motif conductance. Our algorithm works well in different CP structures: including single or multiple CP structure, and local or global CP structures. Results on the synthetic and the empirical networks validate the high performance of our method.