Characterizing the Directness of Accessibility Among Heterogeneous Urban Amenities with Network First Passage Distances

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 emotional and physical well-being of its residents. Measures aiming to capture urban accessibility or vitality through structural factors must account for heterogeneity that is both spatial -- the density and diversity of amenities across space -- and topological -- the connectivity among different types of amenities along the street network. Given that existing measures often only focus on these factors individually, here we develop a simple, principled, and flexible framework to characterize the directness of accessibility among heterogeneous amenities in a city, which we call the Class First Passage Difference (CFPD). The CFPD quantifies the excess travel distance incurred when using the street network to route between different pairs of amenity types, summarizing both the spatial and topological correlations among amenities in a city. Our method exhibits significant statistical associations with a variety of urban prosperity and accessibility indicators when compared to an appropriate null model that scrambles the correlations among the amenities. We also find a clear separation in the CFPD characteristics of cities according to their level of development and geographic region. Our framework provides a principled, interpretable, complementary perspective to existing indices of urban accessibility and vitality.