Time evolution of the average distance DV (t) between phone users in the city and the values of the dilatation index µ = max DV (t)/min DV (t) for the 31 Spanish metropolitan areas studied.
(a) Illustration of the time evolution of DV in three urban areas: Madrid, Sevilla and Zaragoza. This distance DV is equal to the average of the distances between each pair of cells weighted by the density of each of the cells. The resulting distance is then divided by the typical spatial size of the city (given by the square root of the city's area) in order to compare the curves across cities. (b) Rank-size distribution of the dilatation index µ in the 31 metropolitan areas. This figure was created with R and LibreOffice Draw.