Percolation and Topological Properties of Temporal Higher-order Networks

Abstract

Many complex systems that exhibit temporal non-pairwise interactions can be represented by means of generative higher-order network models. Here, we propose a hidden variables 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.

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Cited by in corpus (10)

• Turing pattern theory on homogeneous and heterogeneous higher-order temporal network system
• The simpliciality of higher-order networks
• Percolation-induced PT symmetry breaking
• Multiplex measures for higher-order networks
• The structural evolution of temporal hypergraphs through the lens of hyper-cores
• Higher-order evolutionary dynamics with game transitions
• Higher-order triadic percolation on random hypergraphs
• Dynamical fluctuations of random walks in higher-order networks
• Emerging Activity Temporal Hypergraph: a model for generating realistic time-varying hypergraphs
• Higher-order shortest paths in hypergraphs