Publication : t17/163

Abstract:
We study structural properties of street networks from 97 of the most populous cities worldwide at scales significantly larger than previous studies. We find that the distribution of betweenness centrality (BC), a global structural metric based on network flow, is invariant in all studied street networks, despite the obvious structural differences between them. We also find that the BC distribution is robust to major alterations in the network, including significant changes to its topology and edge weight structure, indicating that the only relevant factors shaping the distribution are the number of nodes in a network, the number of edges, and the constraint of planarity. Through a combination of simulations of random planar graph models and analytical calculations on Cayley trees, this remarkable invariance is demonstrated to be a consequence of a bimodal regime consisting of an underlying tree structure for high betweenness nodes, and a low betweenness regime arising from the presence of loops providing local path alternatives. Furthermore, the high betweenness nodes display a non-trivial spatial dependence, with increasing spatial correlation as a function of the number of roads, leading them to cluster around the barycenter for cities with high density of streets. As the BC is a static predictor of traffic flow, this invariance has important implications for urban planning; indeed, as long as planarity is conserved, bottlenecks will persist and the effect of planned interventions to alleviate congestion will be limited primarily to load redistribution, a feature confirmed by analyzing 200 years of data for central Paris.

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