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The dynamic nature of percolation on networks with triadic interactions

Author

Listed:
  • Hanlin Sun

    (Queen Mary University of London)

  • Filippo Radicchi

    (Indiana University)

  • Jürgen Kurths

    (Potsdam Institute for Climate Impact Research
    Humboldt University of Berlin)

  • Ginestra Bianconi

    (Queen Mary University of London
    The Alan Turing Institute, The British Library)

Abstract

Percolation establishes the connectivity of complex networks and is one of the most fundamental critical phenomena for the study of complex systems. On simple networks, percolation displays a second-order phase transition; on multiplex networks, the percolation transition can become discontinuous. However, little is known about percolation in networks with higher-order interactions. Here, we show that percolation can be turned into a fully fledged dynamical process when higher-order interactions are taken into account. By introducing signed triadic interactions, in which a node can regulate the interactions between two other nodes, we define triadic percolation. We uncover that in this paradigmatic model the connectivity of the network changes in time and that the order parameter undergoes a period doubling and a route to chaos. We provide a general theory for triadic percolation which accurately predicts the full phase diagram on random graphs as confirmed by extensive numerical simulations. We find that triadic percolation on real network topologies reveals a similar phenomenology. These results radically change our understanding of percolation and may be used to study complex systems in which the functional connectivity is changing in time dynamically and in a non-trivial way, such as in neural and climate networks.

Suggested Citation

  • Hanlin Sun & Filippo Radicchi & Jürgen Kurths & Ginestra Bianconi, 2023. "The dynamic nature of percolation on networks with triadic interactions," Nature Communications, Nature, vol. 14(1), pages 1-9, December.
    • Handle: RePEc:nat:natcom:v:14:y:2023:i:1:d:10.1038_s41467-023-37019-5
    DOI: 10.1038/s41467-023-37019-5
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    References listed on IDEAS

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    1. Sergey V. Buldyrev & Roni Parshani & Gerald Paul & H. Eugene Stanley & Shlomo Havlin, 2010. "Catastrophic cascade of failures in interdependent networks," Nature, Nature, vol. 464(7291), pages 1025-1028, April.
    2. Stefan Boettcher & Vijay Singh & Robert M. Ziff, 2012. "Ordinary percolation with discontinuous transitions," Nature Communications, Nature, vol. 3(1), pages 1-5, January.
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    Cited by:

    1. Liang, Yuan & Qi, Mingze & Huangpeng, Qizi & Duan, Xiaojun, 2023. "Percolation of interlayer feature-correlated multiplex networks," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    2. Krishnagopal, Sanjukta & Bianconi, Ginestra, 2023. "Topology and dynamics of higher-order multiplex networks," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).

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