Fig. 2
Analysis of the evolution of the mean value of mmix vs. the fraction of cross-links Γ. In a we show the R2 values obtained when fitting “small” (orange line, square-root fit) and “large” (blue line, linear fit) municipalities, where small and large is meant according to the trial threshold θ over the population N. The dashed zone identifies where the two curves intersect each other, determining the optimized criterion by which we split the whole database in two subsets, one for each type of city. b Presents the same information of a but focusing on densities rather than their extensive counterparts. That is, the trial threshold θ distinguishes between “sparse” (orange line, square-root fit) and “dense” (blue line, linear fit) municipalities. In c, e we report data (bullets) and the best fits (solid lines) for the small and the large municipalities, respectively; in the former the best fit is given by a square-root function with R2 = 0.99 and in the latter the best fit is given by a linear function with R2 = 0.98. These results were corroborated by checking that, in a log–log scale, the best fits are provided by linear functions with slope consistent with 1/2 and 1, respectively. d, f are built analogously, using density rather than population to discriminate between small and large municipalities, and the best fits are given by, respectively, a square-root function with R2 = 0.98 and a linear function with R2 = 0.96. Again, we successfully checked fits also in a log–log scale
