Time Evolution of Road Networks

Urbanization is a fundamental phenomenon which however still remains poorly quantitatively characterized. An important facet of this phenomenon is the road network which co-evolves with other urban structures and we review here the most recent results about the structure and the evolution of these important infrastructures. These studies suggest that the natural evolution of a road network is governed by two elementary processes: (i) 'densification', which corresponds to an increase in the local density of roads around existing central points and (ii) 'exploration' which consists in new roads triggering the spatial evolution of the urbanization front. However, interventions of central, top-down planning could modify this simple picture of a natural evolution and we will present the example of the street network of Paris (France), which during the nineteenth century experienced large modifications supervised by a central authority, the 'Haussmann period'. In this case, the usual network measures display a smooth behavior and the most important quantitative signatures of central planning are the spatial reorganization of centrality and the modification of the block shape distribution. Such effects can only be obtained by structural modifications at a large-scale level, with the creation of new roads not constrained by the existing geometry. These different results suggest that the evolution of a road network results from the superimposition of continuous, local growth processes and punctual changes operating at large spatial scales, opening new directions for the modelling of these systems.