Optimization of flow and cascading effects in weighted complex networks

We investigate the effect of edge weighting scheme $\sim $(k$_{i}$.k$_{j})^{\beta }$ on the optimality of flow efficiency and robustness in complex networks. We achieve this by analyzing a simple distributed flow model: current flow in resistor networks. In this scenario the centrality measure of a node (edge) is given by the current-flow betweenness, that is the amount of current flowing through the node (edge), averaged over all source-target pairs, when unit current enters simultaneously at each node and flows towards a randomly chosen target. The largest loads formed on either the nodes or the edges set the maximum amount of input current for which the network is still congestion free. These two optimal values do not occur for the same value of $\beta $. As congestion may appear on nodes as well as on edges, we also study the cascading behavior of networks, triggered by the removal of one or more entities.