Scaling of Street Network Centrality with City Population

Abstract

Urban scaling laws reveal how cities evolve as their populations grow, yet the role of street network accessibility in this process remains underexplored. We analyze over 5,000 Brazilian cities to establish a scaling law linking average closeness centrality $\langle c_C\rangle$ -- a measure of structural accessibility in street networks-to population size N . Our results demonstrate that $\langle c_C\rangle$ decays sublinearly as $N^{-σ}$ ($σ\approx 0.38$), indicating that larger cities redistribute accessibility from cores to peripheries while maintaining navigability through hierarchical shortcuts. This scaling arises from the fractal interplay between infrastructure and population, characterized by a network dimension $d \approx 2.17$, which exceeds that of a 2D grid. The slower decline in closeness centrality ($σ< 0.5$) reflects a trade-off: urban expansion reduces proximity but enhances connectivity through optimized path diversity, fostering economic dynamism. By integrating the Molinero & Thurner model with network centrality metrics, we provide a framework to reconcile infrastructure efficiency with equitable accessibility in growing cities.