Robustness of networks with dependence clusters against hybrid cascading failure induced by fluctuating load

The overload failures of nodes and the dependency between nodes during the cascading process have a great impact on the robustness of the network. Cascading failure in real-world functional networks are usually caused by extreme values of instantaneous fluctuating load that exceed the allowable range. In order to analyze the combined effects of fluctuating load and the inter-node dependency on the robustness of the network, a hybrid cascading failure model is proposed. Since the load transmission in the network is not random, the biased random walker model based on Quasi-Laplacian centrality in this paper is utilized to describe the fluctuating load, and the inequality of the dependency relationships among nodes within the dependence clusters is considered, and the collapse threshold ρ is introduced to describe the vulnerability of the dependence clusters. The effects of bias parameter, capacity parameter, average size of dependence clusters, and collapse threshold on network robustness are analyzed. The simulation results reveal that nodes with larger centrality have lower probability of extreme events compared to nodes with smaller centrality. Dependence clusters in a network can accelerate the rate of cascading failure, and the inequality of dependency relationship makes the average size of dependence clusters affect networks of different sizes differently.