Optimal network topology for structural robustness based on natural connectivity

The structural robustness of the infrastructure of various real-life systems, which can be represented by networks, is of great importance. Thus we have proposed a tabu search algorithm to optimize the structural robustness of a given network by rewiring the links and fixing the node degrees. The objective of our algorithm is to maximize a new structural robustness measure, natural connectivity, which provides a sensitive and reliable measure of the structural robustness of complex networks and has lower computation complexity. We initially applied this method to several networks with different degree distributions for contrast analysis and investigated the basic properties of the optimal network. We discovered that the optimal network based on the power-law degree distribution exhibits a roughly “eggplant-like” topology, where there is a cluster of high-degree nodes at the head and other low-degree nodes scattered across the body of “eggplant”. Additionally, the cost to rewire links in practical applications is considered; therefore, we optimized this method by employing the assortative rewiring strategy and validated its efficiency.