Network robustness and graph topology
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This paper looks at the network robustness problem from a new perspective. Inspired by Darwin's survival value, a graph-theoretical metric, betweenness, in combination with network weight matrix is used to define a global quantity, network criticality, to characterize the adaptability of a network to the changes in network conditions. We show that network criticality can be interpreted as the average cost of a journey between any two nodes of a network, or as the average of link betweenness sensitivity of a network. We investigate communication networks in particular, and show that in order to maximize the carried load of a network, one needs to minimize network criticality. We show that network criticality is a monotone decreasing and strictly convex function of weight matrix. This leads to a well-defined convex optimization problem to find the optimal weight matrix assignment. We investigate the solution of this optimization problem for the weight assignment and compare our results with existing methods.