Figure 1: The number of social ties as function of grid sizes and urban mobility limits.
From: Urban characteristics attributable to density-driven tie formation
The number of ties T(ρ) plotted as a function of ρ for various grid sizes N. The data points represent the average over n=30 realizations of the simulation described in the text, while the solid green line is the theoretical expression equation (5). The dashed line is a fit to the form 
. As can be seen in each case the agreement between theory and simulation is excellent. The best fit to the scaling exponent yields a value of β≈1.15 independent of N. Note that the measured value of the exponent in empirical data is 1.1≤β≤1.3.
