基于节点重要度动态评估的复杂网络级联失效分析

级联失效前的评估和检测是预防和控制级联失效现象的关键，对充分把握整个网络系统的稳定运行至关重要。为深入探究级联失效传播过程的内在机理，提出一种考虑网络动态特性的节点重要度评估模型；在此基础上，采用一种更符合真实复杂系统的非线性容量负载模型，利用该模型进行不同攻击策略下的级联失效仿真，以网络的最大连通子图比例为测度量化网络抵御级联失效的抗毁性，仿真结果表明，节点41所在的广安市与节点55所在的重庆市，无论是在静态节点重要度评估，还是动态节点重要度评估下，均是成渝铁路网络中最关键的节点；此外，不考虑级联失效情况下，在网络的静态拓扑结构中，节点的度中心性更能代表节点的关键程度；而在动态的网络拓扑结构中，节点的介数中心性更能代表节点的重要性，与度值攻击相比，采用重要度攻击策略能以更快的速度击溃网络；考虑级联失效情况下，与其他攻击策略比较，采用重要度攻击策略时，在级联失效的作用下，仅攻击2个节点，网络便会迅速崩溃，验证了节点重要度动态评估模型的有效性；同时探讨了网络在不同模型参数下抵御级联失效的抗毁性，实验结果表明，在一定范围内提高负载系数、容量系数可以有效提高网络抵制级联失效的抗毁性；受网络拓扑结构和攻击策略的影响，需设置较大的节点容量，来预防网络的级联失效。

Complex network cascade failure analysis based on dynamic evaluation of node importance

Evaluation and detection before cascade failure is the key to prevent and control the cascade failure phenomenon, which is crucial to fully grasp the stable operation of the whole network system. In order to investigate the intrinsic mechanism of cascade failure propagation process, a node importance assessment model considering the dynamic characteristics of the network is proposed; on this basis, a nonlinear capacity load model, which is more consistent with the real complex system, is used to simulate the cascade failure under different attack strategies, and the maximum connectivity subgraph ratio of the network is used as a measure to quantify the resistance of the network to cascade failure, and the simulation results show that that the city of Guang''an, where node 41 is located, and the city of Chongqing, where node 55 is located, are the most critical nodes in the Chengdu-Chongqing railroad network, both under static node importance assessment and dynamic node importance assessment; In addition, without considering cascade failure, in the static topology of the network, the degree centrality of nodes is more representative of the criticality of nodes; while in the dynamic network topology, the mesoscopic centrality of nodes is more representative of the importance of nodes, and the importance attack strategy can collapse the network faster than the degree attack; considering cascade failure, compared with other attack strategies, the When the importance attack strategy is adopted, the network will collapse rapidly when only 2 nodes are attacked under the effect of cascade failure, which verifies the effectiveness of the dynamic evaluation model of node importance; the destructive resistance of the network to resist cascade failure under different model parameters is also explored, and the experimental results show that increasing the load factor and capacity factor within a certain range can effectively improve the destructive resistance of the network to resist cascade failure; subject to network topology and attack strategy, a larger node capacity needs to be set to prevent the cascade failure of the network.