Detecting Core-Periphery Structures by Surprise

TL;DR

This paper introduces a novel statistical method based on surprise to detect core-periphery and bipartite structures in complex networks, enhancing mesoscale structure identification beyond traditional community detection.

Contribution

It proposes a modified surprise measure using a multinomial hypergeometric distribution to identify bimodular structures like core-periphery and bipartite networks.

Findings

Successfully applied to social, economic, and financial networks

Effectively detects core-periphery and bipartite structures

Provides statistically significant p-values for identified structures

Abstract

Detecting the presence of mesoscale structures in complex networks is of primary importance. This is especially true for financial networks, whose structural organization deeply affects their resilience to events like default cascades, shocks propagation, etc. Several methods have been proposed, so far, to detect communities, i.e. groups of nodes whose connectivity is significantly large. Communities, however do not represent the only kind of mesoscale structures characterizing real-world networks: other examples are provided by bow-tie structures, core-periphery structures and bipartite structures. Here we propose a novel method to detect statistically-signifcant bimodular structures, i.e. either bipartite or core-periphery ones. It is based on a modification of the surprise, recently proposed for detecting communities. Our variant allows for bimodular nodes partitions to be revealed, by letting links to be placed either 1) within the core part and between the core and the periphery parts or 2) just between the (empty) layers of a bipartite network. From a technical point of view, this is achieved by employing a multinomial hypergeometric distribution instead of the traditional (binomial) hypergeometric one; as in the latter case, this allows a p-value to be assigned to any given (bi)partition of the nodes. To illustrate the performance of our method, we report the results of its application to several real-world networks, including social, economic and financial ones.