Hypernetwork science via high-order hypergraph walks

• Published in: EPJ data science 2020-06, Vol.9 (1), p.16-34, Article 16
• Main Authors: Aksoy, Sinan G., Joslyn, Cliff, Ortiz Marrero, Carlos, Praggastis, Brenda, Purvine, Emilie
• Format: Article
• Language: English
• Subjects: Clustering; Co authorship; Complexity; Computer Appl. in Social and Behavioral Sciences; Computer Science; Data science; Data-driven Science; Generative model; Graph representations; Graph theory; High-order walk; Hypergraph; hypergraphs, network analysis, generative model, hypergraph models; MATHEMATICS AND COMPUTING; Modeling and Theory Building; Regular Article; Structured data
• ISSN: 2193-1127; 2193-1127
• DOI: 10.1140/epjds/s13688-020-00231-0

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.