Robustness of interdependent networks based on bond percolation

Abstract

Understanding the robustness of interdependent networks has attracted much attention in recent years. In many real scenarios, links may fail instead of nodes and how the interdependent networks behave in this case has not been adequately addressed. In this work, we investigate the link failures propagation mechanism for both two-layer and n-layer interdependent networks by using the self-consistent probabilities method which significantly simplifies the mathematical analysis of such systems. For bond percolation in which initial link failures occur in one layer, we find, analytically and via simulations, that the critical percolation threshold, pc, of this system is lower than that of site percolation. Furthermore, for interdependent ER networks, in contrast to site percolation, bond percolation results show that pc varies nonlinearly with the inverse of average degree. We also find, for the case of bond percolation where initial link failures occur in all layers, that the critical percolation threshold is the same as that of site percolation, but the behavior of the giant component above pc is different. Our research brings insight to better understand the vulnerability of interdependent networks due to link failures.