Higher-order shortest paths in hypergraphs.

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 nondyadic, 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 characterize higher-order connectivity and quantify the relevance of nondyadic ties for efficient shortest paths in a diverse set of empirical networks with and without temporal information. By comparing our results with simple randomized null models, our analysis presents a nuanced picture, suggesting that nondyadic 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 organization of systems with higher-order interactions.