Vulnerability assessment—a critical issue for networks—attempts to foresee unexpected destructive events or hostile attacks in the whole system. In this article, we consider a new Markov global connectivity metric—Kemeny constant, and take its derivative called Markov criticality to identify critical links. Markov criticality allows us to find links that are most influential on the derivative of Kemeny constant. Thus, we can utilize it to identity a critical link ( i , j ) from node i to node j , such that removing it leads to a minimization of networks’ global connectivity, i.e., the Kemeny constant. Furthermore, we also define a novel vulnerability index to measure the average speed by which we can disconnect a specified ratio of links with network decomposition. Our method is of high efficiency, which can be easily employed to calculate the Markov criticality in real-life networks. Comprehensive experiments on several synthetic and real-life networks have demonstrated our method’s better performance by comparing it with state-of-the-art baseline approaches.

中文翻译：

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基于马尔可夫临界度的网络脆弱性测量

漏洞评估（网络的一个关键问题）试图预测整个系统中的意外破坏性事件或恶意攻击。在本文中，我们考虑一个新的马尔可夫全局连通性度量——Kemeny 常数，并将其导数称为马尔可夫临界识别关键链接。马尔可夫临界允许我们找到对 Kemeny 常数的导数影响最大的链接。因此，我们可以利用它来识别关键链接（一世,j) 从节点一世到节点j，因此删除它会导致网络的全局连接性最小化，即 Kemeny 常数。此外，我们还定义了一个新的漏洞指数来衡量我们可以通过网络分解断开指定比例的链接的平均速度。我们的方法效率高，可以很容易地用于计算现实网络中的马尔可夫临界值。通过与最先进的基线方法进行比较，对几个合成网络和现实网络的综合实验证明了我们的方法具有更好的性能。