Efficient disintegration strategies with cost constraint in complex networks: The crucial role of nodes near average degree.

The study of network disintegration, including controlling disease spread and destroying terrorist organizations, has wide application scenarios and attracts many researchers. In this paper, we concentrate on the network disintegration problem with heterogeneous disintegration cost, where the disintegration cost to eliminate each node might be non-identical. We first put forward a disintegration cost model and an optimization model for disintegration strategy. Then, we analyze the hub strategy, leaf strategy, and the average degree strategy to investigate the nodes tendency of the optimal disintegration strategy. Numerical experiments in three synthetic networks and real-world networks indicate that the disintegration effect of hub strategy drops gradually when the disintegration cost changes from homogeneity to heterogeneity. For the situation of strong heterogeneity of disintegration cost of each node, average degree strategy achieves the maximum disintegration effect gradually. Also, taking another perspective, average degree strategy might enlighten efficient solutions to protect critical infrastructure through strengthening the nodes which are chosen by the average degree strategy.