Most of the existing cascading failure models directly quantify the initial load of the node according to its degree or betweenness; this quantification method is suitable for telecommunication network, power grid, or social network.
the node [v.sub.2b] would also fail, which triggers the cascading failure process and causes a new round of load redistribution (red dashed line in Figure 1).
With the consideration of cascading impacts, it could be observed that a larger G would imply less damage caused by the attack on the network.
Figure 5 shows the changing trend of cascading invulnerability in C2 networks along with attacking ratios for different values of [alpha], where 50 rounds of simulations and average calculations are carried out.
In particular, when p > 0.2, almost all nodes in the C2 networks failed as a result of the cascading effect.
To analyze the impact of initial load adjustment coefficients [lambda] and [gamma] on the ability to resist cascading failures, the values of the coefficients A and y are chosen from the range [0,2].
Meanwhile, when both [lambda] and [gamma] are larger than 1, the robustness of C2 networks against cascading failures would be improved significantly.
To analyze the impact caused by the load redistribution coefficient [eta] on C2 networks resistance-cascading failures, G and CF are still employed to measure cascading invulnerability of C2 networks.
Subsequently, the destructiveness of cascading failures could be reduced and the "avalanche" phenomenon could be prevented.
Effect of the Tolerance Parameter [beta] on Network Cascading Invulnerability.
Consequently, the damage caused by cascading failures could be gradually reduced.
After analyzing the effect of each parameter in the cascading failure model on the invulnerability of C2 networks, the optimal value of each parameter is fixed.