Using the Weighted Rich-Club Coefficient to Explore Traffic Organization in Mobility Networks

The aim of a transportation system is to enable the movement of goods or persons between any two locations with the highest possible efficiency. This simple principle inspires highly complex structures in a number of real-world mobility networks of different kind that often exhibit a hierarchical organization. In this paper, we rely on a framework that has been recently introduced for the study of the management and distribution of resources in different real-world systems. This framework offers a new method for exploring the tendency of the top elements to form clubs with exclusive control over the system's resources. Such tendency is known as the weighted rich-club effect. We apply the method to three cases of mobility networks at different scales of resolution: the US air transportation network, the US counties daily commuting, and the Italian municipalities commuting datasets. In all cases, a strong weighted rich-club effect is found. We also show that a very simple model can account for part of the intrinsic features of mobility networks, while deviations found between the theoretical predictions and the empirical observations point to the presence of higher levels of organization.