Quantifying the topological similarities of different parts of urban road networks (URNs) enables us to understand the urban growth patterns. While conventional statistics provide useful information about characteristics of either a single node's direct neighbors or the entire network, such metrics fail to measure the similarities of subnetworks considering local indirect neighborhood relationships. In this study, 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 intra-city spatial homogeneity is highly associated with socioeconomic statuses such as GDP and population growth. Moreover, inter-city spatial homogeneity obtained by transferring the model across different cities, reveals the inter-city similarity of urban network structures originating in Europe, passed on to cities in the US and Asia. Socioeconomic development and inter-city similarity revealed using our method can be leveraged to understand and transfer insights across cities. It also enables us to address urban policy challenges including network planning in rapidly urbanizing areas and combating regional inequality.
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