Abstract: Current researches on anti-attack of complex networks arc based on the hypothesis that all the attacks wouldn't spend any cost. However,most of the complex networks are fragile in confronting selective attack strategies without any cost, which is conflict with real-world networks. Aiming at the contradiction, this paper proposed key indexes, i. c.，the network compactness index and average degree, to measure the attack effects with costs. This paper developed the selective node attack strategies model based on the network compactness index, and ctualitative analysis of the relation between network compactness index, average degree and anti-attack of complex networks.The detailed simulation results show that the key indexes proposed in the paper arc effective; the more compact the network is, and the larger the average degree is, then the more robust the network is; in the same average degrees, the larger the network compactness index is, the more robust the network is.

Key words: Complex networks, Network compactness index, Average degrees, Cost