On robust network planning

One of the important properties of a reliable communication network is the robustness to the environmental changes. This paper looks at the design of robust networks from a new perspective. A graph-theoretical metric, betweenness, in combination with network weight matrix is used to define a global quantity, network criticality, to characterize the robustness of a network. We show that network criticality is a monotone decreasing function of weight matrix. Furthermore, it is shown that network criticality is a strictly convex function of network weight matrix. This leads to a well-defined convex optimization problem to find the optimal weight matrix assignment to minimize network criticality.