AI Insight
This paper presents the first comprehensive survey of 39 different centrality and importance measures for hypergraphs, which are mathematical structures that can model complex higher-order interactions beyond simple pairwise relationships. The authors introduce a novel taxonomy that categorizes these measures into three types: structural (based on network topology), functional (based on impact on system dynamics), and contextual (incorporating external features). The study includes empirical comparisons of these measures' similarities and computational efficiency, providing a unified framework for a previously fragmented field.
Why it matters
Understanding centrality in hypergraphs has important applications in analyzing biological systems, social networks, and other complex systems where interactions involve more than two entities simultaneously. This systematic classification and comparison provides researchers with practical guidance for selecting appropriate measures for their specific applications and identifies gaps for future research.
Understand the Science
⚠️ Preprint – Noch nicht peer-reviewed
Dieser Artikel wurde noch nicht von unabhängigen Experten begutachtet. Die Ergebnisse sind vorläufig und sollten mit Vorsicht interpretiert werden.
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.
Source: A Survey on Centrality and Importance Measures in Hypergraphs: Categorization and Empirical Insights