The effect of attack cost on network robustness

Network robustness is one of the most central topics in the field of complex networks. In this paper, the factor of attack cost associated with network robustness is taken into account. The attack cost is assumed to be positively correlated to the degree of nodes. We found that the performance of different attack strategies is sensitive to the total attack cost. In particular, the high-degree removal strategy (HDRS) is no longer the best attack strategy unless the total attack cost is high. The effect of the assortativity coefficient on the network robustness model with attack cost is extensively investigated. For assortative networks, as the level of assortativity increases, the low-degree removal strategy (LDRS) and the random removal strategy (RRS) are more effective whatever the total attack cost is but HDRS is less (more) effective when the total attack cost is low (high). For disassortative networks, as the level of disassortativity increases LDRS and RRS are less effective whatever the total attack cost is but HDRS is more (less) effective when the total attack cost is low (high). Our work provides insight into the robustness and vulnerability of networked systems with respect to the cost of attack.