Quantifying the spatial homogeneity of urban road networks via graph neural networks

Quantifying the topological similarities of different parts of urban road networks enables us to understand urban growth patterns. Although conventional statistics provide useful information about the characteristics of either a single node’s direct neighbours or the entire network, such metrics fail to measure the similarities of subnetworks or capture local, indirect neighbourhood relationships. Here we propose a graph-based machine learning method to quantify the spatial homogeneity of subnetworks. We apply the method to 11,790 urban road networks across 30 cities worldwide to measure the spatial homogeneity of road networks within each city and across different cities. We find that intracity spatial homogeneity is highly associated with socioeconomic status indicators such as gross domestic product and population growth. Moreover, intercity spatial homogeneity values obtained by transferring the model across different cities reveal the intercity similarity of urban network structures originating in Europe, passed on to cities in the United States and Asia. The socioeconomic development and intercity similarity revealed using our method can be leveraged to understand and transfer insights between cities. It also enables us to address urban policy challenges including network planning in rapidly urbanizing areas and regional inequality. The spatial homogeneity of urban road networks can be quantified in a fine-grained manner with graph neural networks. This method is studied across 11,790 inner-city road networks around the world and can be used to study socioeconomic development and help with urban planning.