Abstract Urban scaling laws reveal how cities evolve as their populations grow, yet the precise quantitative relationship between urban size and spatial proximity influence remains underexplored. We analyze 5252 Brazilian cities to establish a scaling law linking average closeness centrality, c₂ a measure of the influence of spatial proximity on the dissemination of information in street networksto city population size N. Our results demonstrate that c₂ decays sublinearly as N^-, with a characteristic exponent 0. 41. We show that this specific scaling behavior arises from the fractal interplay between infrastructure and population, characterized by an effective network dimension d 2. 20, which exceeds that of a regular 2D grid. The slower decline in closeness centrality \, \, 0. 5 highlights a mitigating effect: while urban growth naturally reduces average spatial proximity, the networks capacity to form topological shortcuts partially preserves navigability and enhances connectivity. By integrating the Molinero Thurner model 1which offers a mechanistic explanation for the observed exponentwith network centrality metrics, our work provides a framework to reconcile infrastructure efficiency with the influence of equitable spatial proximity in growing cities.
Fagundes et al. (Thu,) studied this question.