Bootstrap percolation on hypergraph.

Abstract

Bootstrap percolation is a widely studied model to investigate the robustness of a network for cascading failures. Extensive real-world data analysis has revealed the existence of higher-order interactions among elements, i.e., the interactions beyond pairwise, which are usually described by hypergraphs. In this paper, we propose a generalized bootstrap percolation model on hypergraph, which assumes that the activation of an inactive node depends on the number of active neighbors through its hyperedges. Through numerical simulation and theoretical analysis, we found that the bootstrap percolation threshold and the phase transition type are closely related to the infection threshold and the proportion of higher-order edges. When the infection threshold is significant, for any initial activation probability, the size of the giant active component (GAC) shows continuous growth with increasing occupation probability. When the infection threshold is small, with the increase of the initial activation probability, the size of the GAC changes from continuous growth to discontinuous growth. In addition, we found that in the case of a fixed network average degree, increasing the proportion of higher-order edges will reduce the percolation threshold, which is conducive to enhancing the robustness of the network. At the same time, higher-order edges create more opportunities for inactive nodes to be activated, and increasing the proportion of higher-order edges under the same conditions will change the size of the GAC from continuous growth to discontinuous growth.