阈值和度之间的相关性：一种建模攻击和故障级联的分析方法
Correlations between thresholds and degrees: An analytic approach to model attacks and failure cascades
摘要：
两个节点变量决定了随机网络中级联的演化：节点的度和阈值。两者之间的相关性从根本上改变了网络的鲁棒性，然而，由于顺序统计量的易处理性差，它们在标准分析方法中被忽视为局部树或异质平均场近似。我们展示了它们如何在无限网络大小的热力学极限中变得易于处理。这使得节点攻击的分析描述，其特征在于基于节点度的阈值分配。使用两个例子，我们讨论了可能的影响不规则的相变和不同速度的级联演化的级联控制。
英文摘要：
Two node variables determine the evolution of cascades in random networks: a node's degree and threshold. Correlations between both fundamentally change the robustness of a network, yet, they are disregarded in standard analytic methods as local tree or heterogeneous mean field approximations because of the bad tractability of order statistics. We show how they become tractable in the thermodynamic limit of infinite network size. This enables the analytic description of node attacks that are characterized by threshold allocations based on node degree. Using two examples, we discuss possible implications of irregular phase transitions and different speeds of cascade evolution for the control of cascades.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
