Morphology of travel routes and the organization of cities.

The city is a complex system that evolves through its inherent social and economic interactions. Mediating the movements of people and resources, urban street networks offer a spatial footprint of these activities. Of particular interest is the interplay between street structure and its functional usage. Here, we study the shape of 472,040 spatiotemporally optimized travel routes in the 92 most populated cities in the world, finding that their collective morphology exhibits a directional bias influenced by the attractive (or repulsive) forces resulting from congestion, accessibility, and travel demand. To capture this, we develop a simple geometric measure, inness, that maps this force field. In particular, cities with common inness patterns cluster together in groups that are correlated with their putative stage of urban development as measured by a series of socio-economic and infrastructural indicators, suggesting a strong connection between urban development, increasing physical connectivity, and diversity of road hierarchies.