Estimation of Robustness of Interdependent Networks against Failure of Nodes

Abstract-We consider a partially interdependent network and develop mathematical equations relating the fractional size of the connected component of the network, surviving the cascading failure, to the intra-layer degree distribution of the nodes. We show that these system equations can be mathematically analyzed and closed form expressions for the metrics of robustness can be obtained for the Erdos-Renyi (ER) model of random graph generation. We have described the application of our analysis technique to networks with general degree distributions. In our analysis, we consider the two extremes of the attack model: randomized attack, where nodes are attacked at random without any knowledge of intra-layer degrees and perfect targeted attack, where nodes are attacked based on the strict descending order of their intra-layer degrees. Our results can enable researchers to gain a better understanding of the robustness of interdependent networks.