The relation of effective borders and the significant links of the multi-scale mobility network.
(a) Comparing borders from modularity maximization (blue) with SPT clustering (red) reveals a significant overlap (green). The cumulative topological overlap (see Text S1) is indicating that the SPTD method represents an alternative computational approach to border extraction. (b) The distribution of link significance , defined for each link as the number of shortest-path trees the link appears in, exhibits a strong bimodal distribution. This implies that SPTD can sort links into important or not, and that is approximately a binary variable. (c) By comparing the border structure from SPT clustering with the ensemble of significant links (those that appear in at least half of the shortest-path trees, i.e. in the right half of the histogram in b) we identify topological structures which reveal the core of the network that explains the majority of border locations. This core is represented by the network in blue consisting of star-shaped modules centered around large cities (yellow squares).