Detecting informative higher-order interactions in statistically validated hypergraphs

Federico Musciotto,Federico Battiston,Rosario N Mantegna

doi:10.1038/s42005-021-00710-4

Federico Musciotto, Federico Battiston + Show 1 more

Open Access

https://doi.org/10.1038/s42005-021-00710-4

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Abstract

Recent empirical evidence has shown that in many real-world systems, successfully represented as networks, interactions are not limited to dyads, but often involve three or more agents at a time. These data are better described by hypergraphs, where hyperlinks encode higher-order interactions among a group of nodes. In spite of the extensive literature on networks, detecting informative hyperlinks in real world hypergraphs is still an open problem. Here we propose an analytic approach to filter hypergraphs by identifying those hyperlinks that are over-expressed with respect to a random null hypothesis, and represent the most relevant higher-order connections. We apply our method to a class of synthetic benchmarks and to several datasets, showing that the method highlights hyperlinks that are more informative than those extracted with pairwise approaches. Our method provides a first way, to the best of our knowledge, to obtain statistically validated hypergraphs, separating informative connections from noisy ones.

Highlights

Recent empirical evidence has shown that in many real-world systems, successfully represented as networks, interactions are not limited to dyads, but often involve three or more agents at a time
When we compute the standard deviation of the SC score for the groups highlighted by the Statistically Validated Hypergraph (SVH) and we compare it with that computed (i) on all the groups of justices observed to vote together at least once and (ii) on all possible groups of justices, we find that the groups of justices detected by the SVH have the lowest diversity in liberalism SC score (Fig. 3a)
The SVH approach gives us an insight that is not evident in the raw data or with methods that are limited to the characterization of pairwise interactions: we find that research areas like Nuclear Physics and Physics of Gases and Plasma are similar with respect to the distribution of papers that are written by research groups of different sizes, but the research groups in the two PACS have different publication habits

Summary

Introduction

Recent empirical evidence has shown that in many real-world systems, successfully represented as networks, interactions are not limited to dyads, but often involve three or more agents at a time. Our method works with weighted hypergraphs, where groups of nodes are connected through interactions (hyperlinks) of any size that are not limited to pairwise links.

Results

Conclusion