Cascading failures on complex networks with weak interdependency groups

Abstract

In real complex systems, the overall function is maintained through the connections among nodes. Failures of some nodes may destroy the connectivity of the system and thus damage the function of the system. In some complex systems, some nodes can form “interdependency groups” through hidden interdependency. The failure of one node may damage the rest of the nodes in the interdependency group. In this paper, we investigate the effects of the interdependency strength of the nodes, the size distribution, and the size of the interdependency groups on the cascading dynamics and the robustness of complex networks. Through numerical simulation and theoretical analysis, it is found that the cascading failures of the networks can be divided into two processes at a scale level: “intra-group cascading” and “inter-group cascading”. In the intra-group cascading process, the failure of one node will result in damage to the other nodes in the group through the interdependence among nodes, thus inducing more nodes to be unworkable and resulting in greater destructive force. In the inter-group cascading process, the failed nodes will cause the networks to be fragmented, which leads some nodes outside the interdependency group to isolate from the giant component and go to failure. Under the synergistic effects of these two processes, it is found that there are continuous and discontinuous phase transition phenomena in the cascade dynamics of the network. The occurrence of these two kinds of phase transition phenomena is related to the interdependency strength of nodes, the network degree distribution and the size distribution of the interdependency group. This means that by controlling the characteristics of interdependency groups, such as the interdependence strength of the nodes in the interdependency group or the size distribution of interdependency groups, the system can avoid collapsing suddenly and thus the robustness of the network can be improved.