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arXiv · 2108.03192

Higher-order motif analysis in hypergraphs

Quintino Francesco Lotito·Federico Musciotto·Alberto Montresor·Federico Battiston
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Abstract

A deluge of new data on social, technological and biological networked systems suggests that a large number of interactions among system units are not limited to pairs, but rather involve a higher number of nodes. To properly encode such higher-order interactions, richer mathematical frameworks such as hypergraphs are needed, where hyperlinks describe connections among an arbitrary number of nodes. Here we introduce the concept of higher-order motifs, small connected subgraphs where vertices may be linked by interactions of any order. We provide lower and upper bounds on the number of higher-order motifs as a function of the motif size, and propose an efficient algorithm to extract complete higher-order motif profiles from empirical data. We identify different families of hypergraphs, characterized by distinct higher-order connectivity patterns at the local scale. We also capture evidences of structural reinforcement, a mechanism that associates higher strengths of higher-order interactions for the nodes that interact more at the pairwise level. Our work highlights the informative power of higher-order motifs, providing a first way to extract higher-order fingerprints in hypergraphs at the network microscale.

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Quintino Francesco Lotito, Federico Musciotto, Alberto Montresor, Federico Battiston. 2021-08-06. Higher-order motif analysis in hypergraphs. https://doi.org/10.1038/s42005-022-00858-7

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