Effect of place coordinate randomization on the performance of the rank-distance model.
On the y-axis we present the KL-divergence, , between the empirically observed distribution of displacements in a city and which is the one obtained by the rank-distance model. On the x-axis the probability of randomization, , is depicted. In order to randomize the spatial distribution of places in a city, we iterate through the associated set of places and the coordinates of a place , are randomized with probability . A new pair of coordinates, , is assigned uniformly and within a pre-specified range, where and . corresponds to the case that the original distribution of displacements within a city is maintained, whereas the opposite extreme where equals means that all places have been randomized. The errors bars correspond to standard deviations across cities.