Figure 1

Data analysis framework (a–c) and its application to the case of Chicago (d,e). (a) For a given city, cells in a square grid are grouped into 10 groups according to their traffic volumes \(T_{i}\) in Eq. (3). The traffic volume \(T_{ij}\) and geographic distance \(r_{ij}\) between a cell i of group k (red) and a cell j of group \(k'\) (blue) are identified. (b) Then, the distance exponent \(\gamma _{kk'}\) is estimated using the gravity model in Eq. (5). (c) Estimated values of the distance exponent, i.e., \(\gamma _{kk'}\) for \(k,k'\in \{1,\ldots ,10\}\), form the exponent matrix Γ. (d) Conventional estimation of the distance exponent using the whole set of data for Chicago, resulting in a single distance exponent \(\gamma _{\mathrm{s}}\approx 0.53\) (dashed line) in Eq. (4). (e) Empirical confirmation of multiple gravity laws within Chicago with different values of \(\gamma _{kk'}\) for some cases with \(k=k'\) (dashed lines)