Percolation and Topological Properties of Temporal Higher-order Networks

TL;DR

This paper introduces a formalism to analytically study the topological properties and percolation dynamics of temporal higher-order networks, with applications to social interactions and hypergraph models.

Contribution

It develops a hidden variables framework for higher-order networks and provides analytical tools for their topological analysis and percolation behavior.

Findings

Analytical expressions for topological properties of time-integrated hypergraphs.

Estimates for percolation times in uncorrelated and correlated hypergraphs.

Higher-order interactions significantly affect percolation time estimates in social 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.