Communication and jump size distance distributions. Communication and jump size distance distributions. (A) Communication distance distributions measured in geodesic distance r, PS(r), for all three datasets. Here, r measures the distance between two users when they communicate with each other via either phone calls or SMS. r is measured in the unit of kilometers. (B) Rank distributions PS(r′) for the three datasets follow a power law tail with exponents βr′=0.89 for D1, βr′=1.00 for D2, and βr′=0.64 for D3. (C) Jump size distribution PM(r) measured in geodesic distance r follows a power law distribution. (D) Rank jump size distribution PM(r′) for rank r′ follows a power law distribution with exponent αr′ between 1.2 and 1.3 for D1 and D2 and αr′≈1 for D3. Here we mainly focus on large r (or r′) regime, fitting the tail part of the distributions. For fat-tailed distributions such as power law distributions, the tail part is the most important, determining the convergence/divergence of moments of distributions. The small r (or r′) regime before the peak is often referred to as small value saturations. Dashed lines serve as guide to the eye. Pierre Deville et al. PNAS 2016;113:7047-7052 ©2016 by National Academy of Sciences