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第112行：
第112行： − + − Although scale-free networks are resilient to random failures, we might imagine them being quite vulnerable to targeted hub removal. In this case we consider the robustness of scale free networks in response to targeted attacks, performed with thorough prior knowledge of the network topology. By considering the changes induced by the removal of a hub, specifically the change in the maximum degree and the degrees of the connected nodes, we can derive another formula for the critical threshold considering targeted attacks on a scale free network. − Although scale-free networks are resilient to random failures, we might imagine them being quite vulnerable to targeted hub removal. In this case we consider the robustness of scale free networks in response to targeted attacks, performed with thorough prior knowledge of the network topology. By considering the changes induced by the removal of a hub, specifically the change in the maximum degree and the degrees of the connected nodes, we can derive another formula for the critical threshold considering targeted attacks on a scale free network. 第131行：
第129行： − − This equation cannot be solved analytically, but can be graphed numerically. To summarize the important points, when gamma is large, the network acts as a random network, and attack robustness become similar to random failure robustness of a random network. However, when gamma is smaller, the critical threshold for attacks on scale-free networks becomes relatively small, indicating a weakness to targeted attacks. − − This equation cannot be solved analytically, but can be graphed numerically. To summarize the important points, when gamma is large, the network acts as a random network, and attack robustness become similar to random failure robustness of a random network. However, when gamma is smaller, the critical threshold for attacks on scale-free networks becomes relatively small, indicating a weakness to targeted attacks. − For more detailed information on the attack tolerance of complex networks please see the [[Attack tolerance|attack tolerance page]].+ − − For more detailed information on the attack tolerance of complex networks please see the attack tolerance page. − − 有关复杂网络攻击耐受性的更多详细信息，请参阅攻击耐受性页面。 − −
→Targeted attacks on scale-free networks 无标度网络的针对性攻击
== Targeted attacks on scale-free networks 无标度网络的针对性攻击 ==
==无标度网络的针对性攻击 ==
尽管无标度网络可以抵抗随机故障，但可以想象它对枢纽节点针对性的攻击其实非常脆弱。此时，我们就需要考虑无标度网络对目标攻击的鲁棒性，这需要在充分了解网络拓扑结构的前提下进行。通过研究删除枢纽节点时网络产生的变化，特别是最大程度与所连接节点的程度变化，我们就可以考虑到无标度网络上的针对性攻击，得出临界阈值的另一个公式:
尽管无标度网络可以抵抗随机故障，但可以想象它对枢纽节点针对性的攻击其实非常脆弱。此时，我们就需要考虑无标度网络对目标攻击的鲁棒性，这需要在充分了解网络拓扑结构的前提下进行。通过研究删除枢纽节点时网络产生的变化，特别是最大程度与所连接节点的程度变化，我们就可以考虑到无标度网络上的针对性攻击，得出临界阈值的另一个公式:
</math>
</math>
该方程无法解析求解，但可以用数字表示。从中得出的结论是，当''γ''很大时，该网络可近似看作随机网络，其对抗攻击的鲁棒性变得类似于随机网络的随机故障鲁棒性。但是，当''γ''较小时，针对无标度网络攻击的临界阈值将变得相对较小，其抵抗定向攻击的脆弱性质逐渐显现出来。
该方程无法解析求解，但可以用数字表示。从中得出的结论是，当''γ''很大时，该网络可近似看作随机网络，其对抗攻击的鲁棒性变得类似于随机网络的随机故障鲁棒性。但是，当''γ''较小时，针对无标度网络攻击的临界阈值将变得相对较小，其抵抗定向攻击的脆弱性质逐渐显现出来。
有关[[复杂网络]]攻击耐受性的更多详细信息，请参阅[https://en.wikipedia.org/wiki/Attack_tolerance 攻击耐受性]页面。
== [[级联失效]] ==
== [[级联失效]] ==