Higher-order shortest paths in hypergraphs

TL;DR

This paper introduces a new measure called path size to analyze higher-order connectivity in hypergraphs, revealing the importance of non-dyadic ties for efficient shortest paths in complex networks, especially in time-varying systems.

Contribution

It proposes a novel measure for higher-order connectivity in hypergraphs and provides empirical analysis showing the significance of non-dyadic ties in network connectivity.

Findings

Non-dyadic ties are often central for network connectivity.

Dyadic edges connect more peripheral nodes.

Higher-order interactions are crucial in time-varying systems.

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.