We consider optimal attacks or immunization schemes on different models of random graphs. We derive bounds for the minimum number of nodes needed to be removed from a network such that all remaining components are fragments of negligible size.We obtain bounds for different regimes of random regular graphs, Erdős-Rényi random graphs, and scale free networks, some of which are tight. We show that the performance of attacks by degree is bounded away from optimality.Finally we present a polynomial time attack algorithm and prove its optimal performance in certain cases.

中文翻译：

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复杂网络的最佳粉碎

我们考虑对随机模型的不同模型进行最佳攻击或免疫。我们得出需要从网络中删除的最小节点数的边界，以使所有其余分量都是大小可以忽略的片段。我们获得随机规则图，Erdős-Rényi随机图和无标度网络的不同状态的边界其中很紧。最后证明了多项式时间攻击算法并证明了其在某些情况下的最优性能。