Percolation and Topological Properties of Temporal Higher-Order Networks

Many complex systems that exhibit temporal nonpairwise interactions can be represented by means of generative higher-order network models. Here, we propose a hidden variable formalism to analytically characterize a general class of higher-order network models. We apply our framework to a temporal higher-order activity-driven model, providing analytical expressions for the main topological properties of the time-integrated hypergraphs, depending on the integration time and the activity distributions characterizing the model. Furthermore, we provide analytical estimates for the percolation times of general classes of uncorrelated and correlated hypergraphs. Finally, we quantify the extent to which the percolation time of empirical social interactions is underestimated when their higher-order nature is neglected.Received 1 June 2023Revised 23 October 2023Accepted 11 December 2023DOI:https://doi.org/10.1103/PhysRevLett.132.037401© 2024 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasPercolationPhysical SystemsComplex networksSocial dynamicsSocial networksTechniquesNetwork ModelsStatistical Physics & ThermodynamicsInterdisciplinary Physics