From grids to dendrites: Quantifying spatial heterogeneity in urban road networks

Abstract

Road network spatial heterogeneity significantly influences urban development and infrastructure efficiency. We present a novel approach using Relational Graph Convolutional Networks (RGCN) to analyze road networks across 58 global cities from 2020 to 2024, introducing Hits@1 as a comprehensive measure of spatial heterogeneity. When nodes (Road intersections) exhibit high spatial heterogeneity, they are more diverse and distinct from each other, making the embedding process more straightforward for the RGCN model. A higher Hits@1 score indicates RGCN can better differentiate between nodes, directly correlating with greater spatial heterogeneity in the road network. Our analysis demonstrates that Hits@1 can effectively distinguish four road network typologies (Dendritic, Grid, Mixed, and Polygonal), with Dendritic networks showing the highest heterogeneity (Hits@1$\approx$0.57) and Grid networks the lowest (Hits@1$\approx$0.42). Statistical analysis reveals strong correlations between heterogeneity and urban metrics, including traffic index (R = 0.36), CO2 emissions (R = 0.43), and road density (R = 0.48). Temporal analysis of road evolution shows distinct regional patterns: developing regions trend toward higher heterogeneity, while Western cities demonstrate increasing uniformity. Chinese coastal cities exhibit increasing complexity, contrasting with inland cities’ movement toward organized patterns. These findings validate Hits@1 as an effective metric for understanding road network evolution and provide valuable insights for urban planning.