Optimizing the natural connectivity of scale-free networks using simulated annealing

In real-world networks, the path between two nodes always plays a significant role in the fields of communication or transportation. In some cases, when one path fails, the two nodes cannot communicate any more. Thus, it is necessary to increase alternative paths between nodes. In the recent work (Wu et al., 2011), Wu et al. proposed the natural connectivity as a novel robustness measure of complex networks. The natural connectivity considers the redundancy of alternative paths in a network by computing the number of closed paths of all lengths. To enhance the robustness of networks in terms of the natural connectivity, in this paper, we propose a simulated annealing method to optimize the natural connectivity of scale-free networks without changing the degree distribution. The experimental results show that the simulated annealing method clearly outperforms other local search methods.