🤖 AI Summary
The absence of a unified theoretical framework for identifying core entities in higher-order interaction networks hinders systematic analysis of hypergraph centrality. Method: This paper systematically reviews 39 hypergraph centrality measures and proposes the first structured taxonomy—categorizing them into structural, functional, and contextual classes. Leveraging hypergraph modeling, network dynamical analysis, and empirical evaluation, we characterize systematic differences in similarity patterns and computational complexity across categories. We further construct a reproducible, comparable benchmark suite. Contribution/Results: Our work bridges dual gaps in the field: theoretical integration and empirical validation. The taxonomy provides a methodological guide and technical roadmap for hypergraph analysis, enabling principled, scalable advancement of higher-order network centrality research.
📝 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.
