The transition point of the Chinese multilayer air transportation networks

The air transportation network across a certain area, a typical multilayer complex system, is composed of a number of individual airlines, each of which forms a single layer. A central problem in airline merging is the minimal number of layers, denoted by n(ml), that needed for the merged network to function nearly as well as the fully aggregated network. For this purpose, we monitor several structural measures during the network aggregation process in which n(ml) is gradually increased. For China Air Transportation Network (CATN) we identify a common, sharp transition point yielding n(ml) = 9. Whereas for European Air Transportation Networks (EATN) there is no clear signal of such a transition point. The transition point of CATN is confirmed by means of the Wasserstein distance and the relative entropy. Our results indicate that there is still room in the optimization of CATN while for EATN, it seems better to keep the present structure.