  The spatial configuration of urban amenities and the streets connecting them
collectively provide the structural backbone of a city, influencing its
accessibility, vitality, and ultimately the well-being of its residents. Most
accessibility measures focus on the proximity of amenities in space or along
transportation networks, resulting in metrics largely determined by urban
density alone. These measures are unable to gauge how efficiently street
networks can navigate between amenities, since they neglect the circuity
component of accessibility. Existing measures also often require ad hoc
modeling choices, making them less flexible for different applications and
difficult to apply in cross-sectional analyses. Here we develop a simple,
principled, and flexible measure to characterize the circuity of accessibility
among heterogeneous amenities in a city, which we call the pairwise circuity
(PC). The PC quantifies the excess travel distance incurred when using the
street network to route between a pair of amenity types, summarizing both
spatial and topological correlations among amenities. Measures developed using
our framework exhibit significant statistical associations with a variety of
urban prosperity and accessibility indicators when compared to an appropriate
null model, and we find a clear separation in the PC values of cities according
to development level and geographic region.
