Universal robustness characteristic of weighted networks against cascading failure

We investigate the cascading failure on weighted complex networks by adopting a local weighted flow redistribution rule, where the weight of an edge is (k₈k₉) ^ with k₈ and k₉ being the degrees of the nodes connected by the edge. Assume that a failed edge leads only to a redistribution of the flow passing through it to its neighboring edges. We found that the weighted complex network reaches the strongest robustness level when the weight parameter =1, where the robustness is quantified by a transition from normal state to collapse. We determined 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 obtaining a power-law avalanche size distribution together with a tunable exponent by varying. Our findings have great generality for characterizing cascading-failure-induced disasters in nature.