Fig. 1. The model of percolation of interdependent networks with multiple support-dependence relations. The red node fails after the initial attack. Then the cascading failure process leads to a catastrophiccollapse of the interdependent networks. Finally, only a small fraction of nodes survive.具有多依赖关系的相依网络逾渗示意图, 初始攻击导致红色节点失效, 随后发生级联失效过程, 最终相依网络仅有极少数节点存活

Fig. 2. The model of percolation in interdependent networks with conditional dependency clusters. Nodes in network A randomly depends on ( ) nodes in network B and vice versa. One of the three nodes which node a in network A depends on fails, but the failure proportion does not exceed , node a still works. Two of the three nodes which node b in network B depends on fail, the failure proportion exceeds , node bfails. 相依网络的条件依赖群逾渗模型 A网络节点随机依赖于B网络的 个节点( ), 反之亦然; A网络的a节点依赖的3个节点有一个失效, 但失效比例未超过容忍度 , a节点继续工作; B网络的b节点依赖的节点失效比例超过 , 所以b节点失效

Fig. 3. The results of the percolation of RR-RR interdependent networks for different , each network has 200000 nodes, average degree is 6, . The symbols represent the simulation results, and the solid linesshow the corresponding analytical predictions. (a) The size ofthe giant component versus ; (b) number of iterations. 不同 取值的RR-RR相依网络逾渗, 每个网络节点数 , 平均度 , , 空心标记为仿真值, 实线为逾渗方程数值解 (a) 巨分量 与 对应关系; (b) 级联失效迭代次数(number of iterations, NOI)

Fig. 4. Graphical solutions of ER-ER interdependent networks transition for different . The average degree is 6, . 不同 值对应的ER-ER相依网络相变点, 网络平均度 ,

Fig. 5. The results of the percolation of ER-ER interdependent networks for different , each network has 200000 nodes, average degree is 6, . The symbols represent the simulation results, and the solid linesshow the corresponding analytical predictions. (a) The size ofthe giant component versus ; (b) number of iterations. 不同 取值的ER-ER相依网络逾渗, 每个网络节点数 , 平均度 , , 空心标记为仿真值, 实线为逾渗方程数值解 (a) 巨分量 与 对应关系; (b) 级联失效迭代次数

Fig. 6. The results of the percolation of ER-ER interdependent networks for different dependency degrees, each network has 200000 nodes, average degree is 6. The dependency degrees are (solid symbols) and (empty symbols). (a) The size ofthe giant component versus ; (b) number of iterations. 不同依赖度分布的ER-ER相依网络逾渗, , 分别用实心和空心标记表示, 每个网络节点数 , 平均度 (a) 巨分量 与 对应关系; (b) 级联失效迭代次数

Fig. 7. The critical point versus of ER-ER interdependent networks, The symbols represent the simulation results, and the solid linesshow the corresponding analytical predictions. 不同 取值的ER-ER相依网络相变点, 空心标记为仿真结果, 实线是理论值

Fig. 8. The results of the percolation of SF-SF interdependent networks for different , each network has 200000 nodes, average degree is 6, , . The symbols represent the simulation results, and the solid linesshow the corresponding analytical predictions. (a) The size ofthe giant component versus ; (b) number of iterations. 不同 取值的SF-SF相依网络逾渗, 每个网络节点数 , 平均度 , , , 空心标记为仿真值, 实线为逾渗方程数值解 (a) 巨分量 与 对应关系; (b) 级联失效迭代次数