Algebraic Connectivity Optimization of the Air Transportation Network

In transportation networks the robustness of a network regarding nodes and links failures is a key factor for its design. The goal of this work is to design the most robust network given only the location of each node. A common way to measure the robustness of a network is to evaluate the algebraic connectivity of the graph, which was introduced by Fiedler. Several works solve the maximization of the algebraic connectivity by choosing the weights for the edges in the graph. Other works focus on the best way to add edges in a network in order to optimize the connectivity. In this work we present a practical way to find both the edges and their weights in order to optimize the network robustness. We show that this wider problem which is not currently mentioned in the literature is interesting because the two sub-problems of adding edges and choosing edge weights can not be treated separately. The new combined problem inspired by the air transportation network is formulated and exactly solved in small size network case. For larger size networks, we propose our approximation algorithm and the simulated numerical results are analysed.