From paths to blocks: New measures for street patterns

Abstract

The street network is an important aspect of cities and contains crucial information about their organization and evolution. Characterizing and comparing various street networks could then be helpful for a better understanding of the mechanisms governing the formation and evolution of these systems. Their characterization is however not easy: there are no simple tools to classify planar networks and most of the measures developed for complex networks are not useful when space is relevant. Here, we describe recent efforts in this direction and new methods adapted to spatial networks. We will first discuss measures based on the structure of shortest paths, among which the betweenness centrality. In particular for time-evolving road networks, we will show that the spatial distribution of the betweenness centrality is able to reveal the impact of important structural transformations. Shortest paths are however not the only relevant ones. In particular, they can be very different from those with the smallest number of turns—the simplest paths. The statistical comparison of the lengths of the shortest and simplest paths provides a nontrivial and nonlocal information about the spatial organization of planar graphs. We define the simplicity index as the average ratio of these lengths and the simplicity profile characterizes the simplicity at different scales. Measuring these quantities on artificial (roads, highways, railways) and natural networks (leaves, insect wings) show that the…