Core-periphery detection in hypergraphs

Abstract

Core-periphery detection is a key task in exploratory network analysis where one aims to find a core, a set of nodes well-connected internally and with the periphery, and a periphery, a set of nodes connected only (or mostly) with the core. In this work we propose a model of core-periphery for higher-order networks modeled as hypergraphs and we propose a method for computing a core-score vector that quantifies how close each node is to the core. In particular, we show that this method solves the corresponding non-convex core-periphery optimization problem globally to an arbitrary precision. This method turns out to coincide with the computation of the Perron eigenvector of a nonlinear hypergraph operator, suitably defined in term of the incidence matrix of the hypergraph, generalizing recently proposed centrality models for hypergraphs. We perform several experiments on synthetic and real-world hypergraphs showing that the proposed method outperforms alternative core-periphery detection algorithms, in particular those obtained by transferring established graph methods to the hypergraph setting via clique expansion.

Please cite this paper as:

@article{tudisco2022core,
  title={Core-periphery detection in hypergraphs},
  author={Tudisco, Francesco and Higham, Desmond J},
  journal={arXiv preprint arXiv:2202.12769},
  year={2022}
}

Keywords: Core-periphery meso-scale structure networks hypergraphs Perron-Frobenius theory nonlinear eigenvalues spectral method spectral clustering nonnegative matrices power method