Fig. 1.

Empirical vector fields. a Sketch of the method to build the vector field. Each flow from cell i to j is a vector centered in i, with direction pointing to j and whose modulus is equal to T_ij. Summing vectorially these vectors, we obtain ${\overrightarrow{\mathbf{T}}}_i$ and from it, dividing by the population in i, we get the vector field ${\overrightarrow{\mathbf{W}}}_i$. Commuters vector field W for the London (b) and Paris (c) areas. Colors represent the module of the field $\mid \mid {\overrightarrow{\mathbf{W}}}_i\mid \mid$ per cell