Percolation and topological properties of temporal higher-order networks

Many time-varying networks exhibit non-pairwise interactions that cannot be effectively captured by traditional graph models. Here, we propose a hidden variables formalism to analytically characterize higher-order temporal networks. We apply our framework to a 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 threshold of empirical social interactions is underestimated when their higher-order nature is neglected.

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