加权无标度网络级联抗毁性研究

Invulnerability of Weighted Scale-Free Networks Against Cascading Failure

通过引入一种改进的非线性负载容量模型,对加权无标度网络的级联抗毁性进行了深入研究。采用标准化崩塌规模为度量指标,在局部加权负载重分配准则下,对权重系数、容量参数以及网络密度等参量对网络级联抗毁性的影响进行了数值仿真模拟。结果表明,网络的级联抗毁性随着权重系数θ的增大而降低,在θ≤0.3时网络具有较强的抗毁性,这与线性模型中的结论是截然不同的;网络的级联抗毁性随着容量参数的增大而增强,且在权重系数确定的情况下,存在最优参数组合使得网络具有最强的级联抗毁性。最后,对成本和性能约束下加权无标度网络的级联抗毁性进行了定量分析。

To solve the problem of invulnerability analysis of weighted scale-free networks against cascading failure, an improved nonlinear load-capacity model is introduced. The normalized ava- lanche size is adopted as the measurement of invulnerability, and under the rule of local weighted load redistribution, the influence of weight coefficient, capacity parameters and density of the network on invulnerability of weighted scale-free networks against cascading failure is investiga- ted by numerical simulation. The results demonstrate that the smaller of the weight coefficient 0, the better of the invulnerability, especially when 040.3, which contrasts with the conclusion drawn from the linear model. In addition, the larger of the capacity parameters, the better of the invulnerability. And moreover, when the weight coefficient is fixed, there exists an optimal com- bination of the capacity parameters which ensures that the weighted networks reach the strongest invulnerability level. Finally, the qualitative analysis of invulnerability of weighted scale-free net- works against cascading failure under the restrictions of cost and performance is presented.