Cascading failures on interdependent networks with multiple dependency links and cliques

Cascading failures on interdependent networks have attracted much attention in recent years. In this paper, we study a cascading failure model on interdependent networks with multiple dependency relations and cliques, in which a clique is dependent on multiple cliques in other network and all nodes in the same clique are survive or fail together. Through a percolation theory, we find that the system always undergoes a first order phase transition when the dependency relations are small. The robustness of the system increases with increasing the number of multiple dependency relations between two networks and the size of cliques. The theory can well predict the numerical simulations. (C) 2019 Elsevier B.V. All rights reserved.