Core-periphery structure requires something else in the network

TL;DR

This paper challenges the traditional view of core-periphery structures in networks, arguing they are mainly explained by degree heterogeneity, and proposes a new algorithm to detect core-periphery pairs beyond degree effects.

Contribution

It introduces a scalable algorithm that detects multiple core-periphery pairs in networks while controlling for degree heterogeneity, advancing beyond existing single-core models.

Findings

Traditional core-periphery models are largely explained by degree distribution.

The proposed algorithm can identify multiple core-periphery pairs.

Empirical networks reveal complex core-periphery structures beyond degree effects.

Abstract

A network with core-periphery structure consists of core nodes that are densely interconnected. In contrast to community structure, which is a different meso-scale structure of networks, core nodes can be connected to peripheral nodes and peripheral nodes are not densely interconnected. Although core-periphery structure sounds reasonable, we argue that it is merely accounted for by heterogeneous degree distributions, if one partitions a network into a single core block and a single periphery block, which the famous Borgatti-Everett algorithm and many succeeding algorithms assume. In other words, there is a strong tendency that high-degree and low-degree nodes are judged to be core and peripheral nodes, respectively. To discuss core-periphery structure beyond the expectation of the node's degree (as described by the configuration model), we propose that one needs to assume at least one block of nodes apart from the focal core-periphery structure, such as a different core-periphery pair, community or nodes not belonging to any meso-scale structure. We propose a scalable algorithm to detect pairs of core and periphery in networks, controlling for the effect of the node's degree. We illustrate our algorithm using various empirical networks.