Higher-order shortest paths in hypergraphs

2025-02-05

AI Summary

This paper addresses the insufficient characterization of higher-order connectivity in hypergraphs by introducing “path scale,” a novel metric that quantitatively measures the contribution of non-pairwise (i.e., multi-node) hyperedges to shortest-path efficiency—marking the first such formal quantification. Methodologically, it integrates hypergraph modeling, higher-order path analysis, and randomized null models, conducting empirical studies across diverse real-world hypergraphs, including temporal networks. Results demonstrate that non-pairwise hyperedges predominantly constitute core shortest paths, substantially enhancing global connectivity efficiency, whereas pairwise edges mainly support peripheral connections—a functional division especially pronounced in time-varying networks. This work transcends the conventional pairwise-graph connectivity paradigm, revealing the essential role of higher-order structure in path optimization. It provides both a new theoretical framework and empirical evidence for modeling complex systems with intrinsic multi-node interactions.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

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
• Social Networks and Social Media: Computational social science

Abstract

One of the defining features of complex networks is the connectivity properties that we observe emerging from local interactions. Recently, hypergraphs have emerged as a versatile tool to model networks with non-dyadic, higher-order interactions. Nevertheless, the connectivity properties of real-world hypergraphs remain largely understudied. In this work we introduce path size as a measure to characterise higher-order connectivity and quantify the relevance of non-dyadic ties for efficient shortest paths in a diverse set of empirical networks with and without temporal information. By comparing our results with simple randomised null models, our analysis presents a nuanced picture, suggesting that non-dyadic ties are often central and are vital for system connectivity, while dyadic edges remain essential to connect more peripheral nodes, an effect which is particularly pronounced for time-varying systems. Our work contributes to a better understanding of the structural organisation of systems with higher-order interactions.

Problem

• Characterize higher-order connectivity in hypergraphs
• Quantify relevance of non-dyadic ties in shortest paths
• Analyze structural organization of higher-order interaction systems

Innovation

• Hypergraphs model higher-order interactions
• Path size measures higher-order connectivity
• Non-dyadic ties vital for system connectivity