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

2025-11-27

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.

Technology Category

• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Cognitive Modeling & Cognitive Systems: Social Cognition And Interaction

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

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.

Problem

• Surveying hypergraph centrality measures lacking a unified framework
• Classifying measures into structural, functional, and contextual categories
• Comparing empirical similarity and computation time of measures

Innovation

• Systematic survey of 39 hypergraph centrality measures
• Novel taxonomy categorizing measures as structural, functional, contextual
• Experimental assessment comparing empirical similarity and computation time