The dynamic nature of percolation on networks with triadic interactions

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.

62 pages, 20 figures

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• Information propagation in multilayer systems with higher-order interactions across timescales
• The nature of hypergraph $k$-core percolation problems
• Topology and dynamics of higher-order multiplex networks
• Shortest-path percolation on random networks
• Triadic percolation induces dynamical topological patterns in higher-order networks
• Higher-order triadic percolation on random hypergraphs
• General theory for extended-range percolation on simple and multiplex networks
• Triadic percolation on multilayer networks
• Discontinuous percolation via suppression of neighboring clusters in a network
• Discontinuous transition in explosive percolation via local suppression
• Shortest-path percolation on scale-free networks
• Superstable Geometry in Triadic Percolation