Universal robustness characteristic of weighted networks against cascading failure
Wen-Xu Wang and Guanrong Chen

We investigate the cascading failure on weighted complex networks by adopting a local weighted flow redistribution rule, where the weight of an edge is $(k_i k_j)^\theta$ with $k_i$ and $k_j$ being the degrees of the nodes connected by the edge. Assume that a failed edge only leads to a redistribution of the flow passing through it to its neighboring edges. We found the weighted complex network reaches the strongest robustness level when the weight parameter $\theta =1$, where the robustness is quantified by a transition from normal state to collapse. We figured out that this is a universal phenomenon for all typical network models, such as small-world and scale-free networks. We then confirm by theoretical predictions this universal robustness characteristic observed in simulations. We furthermore explore the statistical characteristics of the avalanche size of a network, thus obtain a power-law avalanche size distribution together with the tunable exponent by varying $\theta$. Our findings have great generality for characterizing cascading-failure-induced disasters in nature.

© 2008 The American Physical Society.