Hyperedge overlap drives explosive transitions in systems with higher-order interactions

Federico Malizia, Santiago Lamata-Otín, Mattia Frasca, Vito Latora () and Jesús Gómez-Gardeñes ()
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Federico Malizia: Northeastern University London
Santiago Lamata-Otín: University of Zaragoza
Mattia Frasca: University of Catania
Vito Latora: University of Catania
Jesús Gómez-Gardeñes: University of Zaragoza

Nature Communications, 2025, vol. 16, issue 1, 1-10

Abstract: Abstract Recent studies have shown that novel collective behaviors emerge in complex systems due to the presence of higher-order interactions. However, how the collective behavior of a system is influenced by the microscopic organization of its higher-order interactions is not fully understood. In this work, we introduce a way to quantify the overlap among the hyperedges of a higher-order network, and we show that real-world systems exhibit different levels of intra-order hyperedge overlap. We then study two types of dynamical processes on higher-order networks, namely complex contagion and synchronization, finding that intra-order hyperedge overlap plays a universal role in determining the collective behavior in a variety of systems. Our results demonstrate that the presence of higher-order interactions alone does not guarantee abrupt transitions. Rather, explosivity and bistability require a microscopic organization of the structure with a low value of intra-order hyperedge overlap.

Date: 2025
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DOI: 10.1038/s41467-024-55506-1

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