The influence of the depth of k-core layers on the robustness of interdependent networks against cascading failures

The hierarchical structure, k-core, is common in various complex networks, and the actual network always has successive layers from 1-core layer (the peripheral layer) to km-core layer (the core layer). The nodes within the core layer have been proved to be the most influential spreaders, but there is few work about how the depth of k-core layers (the value of km) can affect the robustness against cascading failures, rather than the interdependent networks. First, following the preferential attachment, a novel method is proposed to generate the scale-free network with successive k-core layers (KCBA network), and the KCBA network is validated more realistic than the traditional BA network. Then, with KCBA interdependent networks, the effect of the depth of k-core layers is investigated. Considering the load-based model, the loss of capacity on nodes is adopted to quantify the robustness instead of the number of functional nodes in the end. We conduct two attacking strategies, i.e. the RO-attack (Randomly remove only one node) and the RF-attack (Randomly remove a fraction of nodes). Results show that the robustness of KCBA networks not only depends on the depth of k-core layers, but also is slightly influenced by the initial load. With RO-attack, the networks with less k-core layers are more robust when the initial load is small. With RF-attack, the robustness improves with small km, but the improvement is getting weaker with the increment of the initial load. In a word, the lower the depth is, the more robust the networks will be.