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

Author

Listed:
  • Federico Malizia

    (Northeastern University London
    University of Catania)

  • Santiago Lamata-Otín

    (University of Zaragoza
    University of Zaragoza)

  • Mattia Frasca

    (University of Catania)

  • Vito Latora

    (University of Catania
    Queen Mary University of London
    Complexity Science Hub Vienna)

  • Jesús Gómez-Gardeñes

    (University of Zaragoza
    University of Zaragoza)

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.

Suggested Citation

  • Federico Malizia & Santiago Lamata-Otín & Mattia Frasca & Vito Latora & Jesús Gómez-Gardeñes, 2025. "Hyperedge overlap drives explosive transitions in systems with higher-order interactions," Nature Communications, Nature, vol. 16(1), pages 1-10, December.
    • Handle: RePEc:nat:natcom:v:16:y:2025:i:1:d:10.1038_s41467-024-55506-1
    DOI: 10.1038/s41467-024-55506-1
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    References listed on IDEAS

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