Measuring the Time Evolution of Spatial Networks

We discussed in the previous Chaps. ( 1– 6) how to characterize the structure of spatial networks. In many instances, however, these networks are evolving in time, growing, and expanding in space. This is typically the case of transportation networks such as roads, subways, and railways, but also for biological networks. It is therefore important to be able to characterize the evolution of these networks, and to detect crucial changes and distinguish them from ordinary growth. In this chapter, we will address such problems for the road networks and we will try to highlight the major differences between an “organic” growth from systems that experiences major changes due to planning decisions. We will illustrate these two types of evolution on the example of the region of Groane (Italy) and the example of central Paris which experienced major large-scale planning operations during the nineteenth century (the “Haussmann” period). In this latter case, 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. The evolution of the road network thus appears here as resulting from the superimposition of continuous, local growth processes, and punctual changes operating at large spatial scales.