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The vulnerability of complex systems induced by cascade failures revealed the comprehensive interaction of dynamics with network structure. The effect on cascade failures induced by cluster structure was investigated on three networks, small-world, scale-free, and module networks, of which the clustering coefficient is controllable by the random walk method. After analyzing the shifting process of load, we found that the betweenness centrality and the cluster structure play an important role in cascading model. Focusing on this point, properties of cascading failures were studied on model networks with adjustable clustering coefficient and fixed degree distribution. In the proposed weighting strategy, the path length of an edge is designed as the product of the clustering coefficient of its end nodes, and then the modified betweenness centrality of the edge is calculated and applied in cascade model as its weights. The optimal region of the weighting scheme and the size of the survival components were investigated by simulating the edge removing attack, under the rule of local redistribution based on edge weights. We found that the weighting scheme based on the modified betweenness centrality makes all three networks have better robustness against edge attack than the one based on the original betweenness centrality.

Robustness in Weighted Networks with Cluster Structure