Cascading failure analysis and critical node identification in complex networks

Cascading failures in complex networks have attracted widespread attention in recent years. In this paper, a cascade model is proposed to analyze the potential overloads of nodes and edges simultaneously. First, some theoretical results for regular networks are detailed by the cascade model. The results show that in ring networks, as long as the capacity of each node or edge exceeds twice its initial load, the networks still work normally when an arbitrary node or edge breaks down, and in regular networks the failure of the farthest edges is most likely to induce cascades and the robustness of regular networks becomes stronger with the increase in the number of edges. Furthermore, an indicator evaluating the damage of the cascades is introduced. The analysis on the robustness of some typical networks indicates that WS networks can resist cascading failures more effectively and the robustness performance of WS networks can be improved by increasing rewiring probabilities. In BA networks, the failure of a critical node may pull down the whole networks, while the networks still function normally even if any edge breaks down. Finally, a forecasting indicator, called modified betweenness centrality, is proposed to identify critical nodes and experimental results show that the proposed indicator outperforms other typical indicators in identifying critical nodes.