Percolation on simplicial complexes

From human communications to ecological systems, higher-order networks are ubiquitous in our society. The study of their dynamic processes using percolation theory has attracted much attention. Here, we develop a framework for investigating the percolation of simplicial complexes with arbitrary dimensions, where higher-order and pairwise interactions coexist. We assess the robustness of simplicial complexes in detail and calculate some properties of our model analytically, including the size of the giant component, the critical point where the giant component appears, and the critical condition where a double transition occurs. For a high density of simplices, the system exhibits a double transition. In the first transition, there is a discontinuous drop in the size of the giant component. In contrast, all connected components become negligibly small in the second transition, and the giant component disappears.(c) 2022 Elsevier Inc. All rights reserved.