Communicability geometry captures traffic flows in cities

Understanding the structural and dynamical drivers of network flow is an important goal for our complete understanding of complex systems. Particularly challenging is the determination of the routes used by items when flowing through a network. The study of vehicular traffic flow in cities offers a unique opportunity to test theoretical models about network flows and traffic routes using experimental data. Here, we found observational evidence that there is higher vehicular traffic flow through the communicability shortest paths, which assume an ‘all-routes’ flow, than through the shortest paths in four cities of different sizes, populations and geographical locations. The communicability function is derived here from a coarse-grained theory of traffic on networks accounting for an auxiliary vehicular propagation speed. Finally, we study the vehicular ‘all-routes’ flow in cities as the perceptual problem of drivers seeing the shortest paths as ‘too central to be empty’. Akbarzadeh and Estrada mathematically characterize the properties of traffic flow and find that, in four different cities, there is more traffic not through the shortest paths, but through the communicability shortest paths, which assume an ‘all-routes’ flow.