The robustness of interdependent weighted networks

We analysis the cascading failure of interdependent weighted networks based on percolation theory and local weighted flow redistribution rule. The weight of a node is Biθ, where Bi is the betweenness of the node. We assume that the two networks A and B of size NA andNB are BA networks, and suppose two different one-to-one interdependent network, one is random, the other based on nodes' betweenness. Assume that a failed node in network A leads to a redistribution of the flow passing through it to its neighboring nodes and the interdependent node in network B also to be disabled, where the two failure factors happen concurrently, or successively. We find that the one-to-one random interdependent weighted complex network reaches the strongest robustness level when the weight parameter θ =0.5, no matter cascading failure caused by two failure factors happen concurrently, or successively. And when the interdependent relationship based on nodes' betweenness, θ=0.7 to get the strongest robustness level.