Algebraic Connectivity Optimization of Large Scale and Directed Air Transportation Network

In transportation networks the robustness of a network regarding nodes and links failures is a key factor for its design. A common way to measure the robustness of a network is to evaluate its algebraic connectivity. In our previous work we formulated a new air transportation network model and showed the algebraic connectivity optimization problem is important because the two sub-problems of adding edges and choosing edge weights can not be treated separately. We presented a method to find both the edges and the corresponding weights in order to optimize the small scale network algebraic connectivity, which is a measure for robustness. In this paper we propose the cluster decomposition method to solve the larger size network problem. Moreover, the algebraic connectivity optimization for directed air transportation network is discussed. Simulations are performed for both large scale problem and directed network problem.