A Survey on Centrality and Importance Measures in Hypergraphs: Categorization and Empirical Insights

TL;DR

This paper provides a comprehensive survey and taxonomy of 39 hypergraph centrality measures, comparing their empirical similarities and computational efficiency, and discusses future research directions in the field.

Contribution

It introduces a novel taxonomy classifying hypergraph centrality measures and offers the first systematic empirical assessment of their similarities and computational aspects.

Findings

Structural measures are generally faster to compute.

Functional measures show diverse impacts on system dynamics.

Measures vary significantly in empirical similarity.

Abstract

Identifying central entities and interactions is a fundamental problem in network science. While well-studied for graphs (pairwise relations), many biological and social systems exhibit higher-order interactions best modeled by hypergraphs. This has led to a proliferation of specialized hypergraph centrality measures, but the field remains fragmented and lacks a unifying framework. This paper addresses this gap by providing the first systematic survey of 39 distinct measures. We introduce a novel taxonomy classifying them as: (1) structural (topology-based), (2) functional (impact on system dynamics), or (3) contextual (incorporating external features). We also present an experimental assessment comparing their empirical similarity and computation time. Finally, we discuss applications, establishing a coherent roadmap for future research in this area.