Percolation on interdependent networks with cliques and weak interdependence

Abstract

Previous researches on cascading failures on interdependent networks with cliques mainly consider “strong” interdependence, that is, once a clique fails, its dependency partner in the other layer will fail completely. However, many interdependent systems in real-world may have self-sustaining abilities, and the failure of one clique may only destroy part of the function of its dependency partner, which can be called “weak” interdependence. In this paper, based on the framework of percolation, a cascading failure model on the interdependent networks with cliques and weak interdependence is investigated analytically and numerically. The results of extensive simulations show that the type of the phase transitions of both layers can be altered from discontinuous phase transitions to continuous phase transitions with the decrease of interdependence strength. In addition, in the process from discontinuous phase transitions to continuous phase transitions, the whole system exhibits a surprising phenomenon of mixed phase transitions: layer with large size of cliques percolates continuously while layer with small size of cliques percolates discontinuously. It indicates that weak interdependence strength and the structure of cliques can enhance the robustness of the interdependent networks. The theoretical and numerical predictions agree well with each other.