Improving the robustness of spatial networks by link addition: more and dispersed links perform better

It is an effective way to improve network robustness by adding connectivity links. Although some addition strategies have been proposed, the addition cost in spatial networks is still missing. This paper adopts a geographical network model to investigate two different constraint scenarios, revealing better addition mechanisms, i.e., limited addition range (LAR) and limited addition length (LAL). In LAR scenario, f additional connections are added within a certain radius r, while only the total length delta of added links is noticed in LAL scenario. With numerical analysis, some ordinary results are first obtained that the robustness of spatial networks improves as f or delta increases, indicating that more links produce better effects. In LAR, adding long links also works effectively. Besides, a special case of LAR is proposed that adding links intensively for a few nodes, and results show that dispersed addition performs better. In LAL, for each delta, feasible solutions are categorized by different numbers of links n delta, and it is found that large n delta has a significant impact on robustness even though delta gets longer. Although adding either more or long links can improve the robustness of spatial networks, it can be concluded that adding more and short links dispersedly outperforms fewer and long ones intensively.