A Nonlinear Spectral Method for Core--Periphery Detection in Networks

TL;DR

This paper introduces a nonlinear spectral algorithm for detecting core-periphery structures in networks, with proven convergence and scalability, offering advantages over existing methods through theoretical analysis and empirical validation.

Contribution

It develops a novel iterative algorithm based on nonlinear Perron-Frobenius theory for core-periphery detection, with a new interpretation via a logistic random graph model.

Findings

Algorithm converges globally to a unique solution.

Scales linearly with network size, suitable for large networks.

Outperforms current state-of-the-art methods on synthetic and real data.

Abstract

We derive and analyse a new iterative algorithm for detecting network core--periphery structure. Using techniques in nonlinear Perron-Frobenius theory, we prove global convergence to the unique solution of a relaxed version of a natural discrete optimization problem. On sparse networks, the cost of each iteration scales linearly with the number of nodes, making the algorithm feasible for large-scale problems. We give an alternative interpretation of the algorithm from the perspective of maximum likelihood reordering of a new logistic core--periphery random graph model. This viewpoint also gives a new basis for quantitatively judging a core--periphery detection algorithm. We illustrate the algorithm on a range of synthetic and real networks, and show that it offers advantages over the current state-of-the-art.