Identifying maximal sets of significantly interacting nodes in higher-order networks

TL;DR

This paper presents a method to identify maximal groups of nodes that consistently interact in higher-order networks, improving understanding of complex collective behaviors in real-world systems.

Contribution

The paper introduces a novel approach for detecting statistically validated simplices in higher-order networks, enhancing the analysis of collective interactions.

Findings

Effective in identifying maximal interacting sets in benchmarks

Detects simplices with highly similar nodes in real datasets

Provides insights into the generative processes of higher-order networks

Abstract

We introduce a method for the detection of Statistically Validated Simplices in higher-order networks. Statistically validated simplices represent the maximal sets of nodes of any size that consistently interact collectively and do not include co-interacting nodes that appears only occasionally. Using properly designed higher-order benchmarks, we show that our approach is highly effective in systems where the maximal sets are likely to be diluted into interactions of larger sizes that include occasional participants. By applying our method to two real world datasets, we also show how it allows to detect simplices whose nodes are characterized by significant levels of similarity, providing new insights on the generative processes of real world higher-order networks.