Threshold for the Outbreak of Cascading Failures in Degree-Degree Uncorrelated Networks

In complex networks, the size of the giant component formed by unfailed nodes is critically important for estimating the robustness of networks against cascading failures. In order to explore the critical moment of cascading failures break-out, we provide a cascade of overload failure model with local load sharing mechanism and then deduce the threshold of node capacity when the large-scale cascading failures happen and unfailed nodes in steady state cannot connect to each other to form a large connected subnetwork. We get the theoretical derivation of this threshold in degree-degree uncorrelated networks and validate the effectiveness of this method in simulation. This threshold provides us with a guidance to improve the network robustness under the premise of limited capacity resource when creating a network and assigning load. Therefore, this threshold is useful and important to analyze the robustness of networks. We believe that our research provides us with a guidance to improve the network robustness under the premise of limited capacity resource.