Hypernetwork Science via High-Order Hypergraph Walks

TL;DR

This paper introduces high-order hypergraph walks to extend graph network analysis techniques to hypergraphs, revealing complex structures in real-world hypernetworks that are not detectable by traditional graph methods.

Contribution

It develops a framework for hypergraph walks that generalize key graph analysis methods, enabling richer structural insights into hypernetworks.

Findings

Hypergraph walks uncover nuanced structures in real-world data.

Traditional properties like density do not predict hypergraph structural measures.

Hypergraph-native tools reveal phenomena missed by graph-based analyses.

Abstract

We propose high-order hypergraph walks as a framework to generalize graph-based network science techniques to hypergraphs. Edge incidence in hypergraphs is quantitative, yielding hypergraph walks with both length and width. Graph methods which then generalize to hypergraphs include connected component analyses, graph distance-based metrics such as closeness centrality, and motif-based measures such as clustering coefficients. We apply high-order analogs of these methods to real world hypernetworks, and show they reveal nuanced and interpretable structure that cannot be detected by graph-based methods. Lastly, we apply three generative models to the data and find that basic hypergraph properties, such as density and degree distributions, do not necessarily control these new structural measurements. Our work demonstrates how analyses of hypergraph-structured data are richer when utilizing tools tailored to capture hypergraph-native phenomena, and suggests one possible avenue towards that end.