Percolation transitions in simplicial complexes with interdependent relationships

¹ Department of Mathematics, Shanghai University - Shanghai 200444, China
² Qian Weichang College, Shanghai University - Shanghai 200444, China

Received: 23 July 2024
Accepted: 10 December 2024

Abstract

We study higher-order percolation phenomena in two interdependent simplicial complexes. Based on the generating function approach, we develop a theoretical framework that provides insights into the percolation dynamics via pairwise or higher-order 2-simplex interactions among individuals. Our findings reveal that higher-order percolation in such structures displays a richer phase transition behavior than that observed in a single simplicial complex or interdependent dyadic networks. We observe both continuous and discontinuous transitions, which occur with either the removal of a small or large fraction of nodes. The initial phase of the transition, triggered by the removal of a small fraction of nodes, is primarily influenced by the density of triangles in each complex. In contrast, the terminal phase of the transition, during which the giant component disappears, is predominantly determined by the strength of interdependence between two complexes.