Resilience analytics of networks with dependency groups

Dependency property that binds the failure of some network components to the failure of other network components reduces network robustness, the absorptive capacity of network, while the recovery scheme can improve the restorative capacity. However, the effect of both dependency property and recovery scheme on network resilience is seldom addressed. In this paper, we introduce a dependency strength function which describe the way of evolution of dependency strength and select the common spontaneous recovery scheme for networks with dependency groups. Then, based on resilience framework, we investigate the effect of dependency strength and spontaneous recovery probability on network resilience by simulation. Numerical simulations employing the Erdős-Rényi networks show that the dependency strength has little impact on network resilience, and spontaneous recovery probability has a positive correlation with the network resilience. With the increase of time period T, the role of recovery probability in network resilience becomes smaller and smaller. Furthermore, improving the spontaneous recovery probability and the convexity of function of dependency strength significantly reduce the number of iterations of network back to normal operation under low recovery probability.