Cascading failures on complex networks with weak interdependency groups

In real complex systems, the overall function is maintained through the connections among nodes. Failuresof some nodes may destroy the connectivity of the system and thus damage the function of the system. In somecomplex systems, some nodes can form "interdependency groups" through hidden interdependency. The failureof one node may damage the rest of the nodes in the interdependency group. In this paper, we investigate theeffects of the interdependency strength of the nodes, the size distribution, and the size of the interdependencygroups on the cascading dynamics and the robustness of complex networks. Through numerical simulation andtheoretical analysis, it is found that the cascading failures of the networks can be divided into two processes ata scale level: "intra-group cascading" and "inter-group cascading". In the intra-group cascading process, thefailure of one node will result in damage to the other nodes in the group through the interdependence amongnodes, thus inducing more nodes to be unworkable and resulting in greater destructive force. In the inter-groupcascading process, the failed nodes will cause the networks to be fragmented, which leads some nodes outsidethe interdependency group to isolate from the giant component and go to failure. Under the synergistic effectsof these two processes, it is found that there are continuous and discontinuous phase transition phenomena inthe cascade dynamics of the network. The occurrence of these two kinds of phase transition phenomena isrelated to the interdependency strength of nodes, the network degree distribution and the size distribution ofthe interdependency group. This means that by controlling the characteristics of interdependency groups, suchas the interdependence strength of the nodes in the interdependency group or the size distribution ofinterdependency groups, the system can avoid collapsing suddenly and thus the robustness of the network can be improved