The eigenvector centrality of hypergraphs

TL;DR

This paper introduces a new eigenvector centrality measure for hypergraphs, extending previous concepts to non-uniform cases and demonstrating its effectiveness on real-world data.

Contribution

It defines an adjacency tensor for hypergraphs and proposes a generalized eigenvector centrality applicable to both uniform and non-uniform hypergraphs.

Findings

The proposed centrality reduces to Benson's for uniform hypergraphs.

It reduces to the eigenvector centrality of graphs when edges contain two vertices.

Experiments show the measure effectively identifies important vertices.

Abstract

A hypergraph is called uniform when every hyperedge contains the same number of vertices, otherwise, it is called non-uniform. In the real world, many systems give rise to non-uniform hypergraphs, such as email networks and co-authorship networks. A uniform hypergraph has a natural one-to-one correspondence with its adjacency tensor. In 2019, Benson proposed the eigenvector centrality of uniform hypergraphs via its adjacency tensor. In this paper, we define an adjacency tensor for hypergraphs and propose the eigenvector centrality for hypergraphs. When the hypergraph is uniform, our proposed eigenvector centrality reduces to Benson's. When each edge of the uniform hypergraph contains exactly two vertices, our proposed centrality reduces to the eigenvector centrality of graphs. We conducted experiments on several real-world hypergraph datasets. The results show that, compared to traditional centrality measures, the proposed centrality measure provides a unique perspective for identifying important vertices and can also effectively identify them.