Fig. 3
From: Quantifying the non-isomorphism of global urban road networks using GNNs and graph kernels
URN Comparison. We utilized EdgeCNN to classify nodes within intercity road networks. In these visualizations, blue represents a node classification accuracy of 0.0, while red indicates an accuracy of 1.0. The gradient of color reflects the varying levels of node classification accuracy. Our analysis included two European cities: Frankfurt (average non-isomorphism rate of 0.777) and Warsaw (0.798); two North American cities: Los Angeles (0.873) and Mexico City (0.881); and two Asia-Pacific cities: Seoul (0.830) and Tokyo (0.887). (a) Comparison between Frankfurt and Warsaw (non-isomorphism rate 0.592). The overall lighter color indicates smaller differences, with only the road networks on the north and south sides of the Main River in Frankfurt being less regular. (b) Comparison between Los Angeles and Frankfurt (0.745). The slightly darker color compared to panel a suggests minor differences in the overall road network. (c) Comparison between Tokyo and Seoul (0.735). The lighter color in the areas north of the Han River in Seoul and near Tokyo Bay indicates smaller differences. (d) URN Relationship Network. We selected intercity relationships with a non-isomorphism rate \(\le 0.78\). Chicago, Dubai, Toronto, and Jakarta do not appear in the panel because their non-isomorphism rate with other cities exceeded 0.78, partly due to the higher regularity of their road networks. (e) Comparison between Frankfurt and Mexico City (0.956). Compared to panel (a), the city center areas remain lighter in color, but the surrounding areas are noticeably darker. This suggests that while Mexico City’s road network is generally more regular, its historical city center, with numerous cultural landmarks such as Constitution Square, exhibits lower regularity due to the challenges of significant renovations. (f, g) Comparisons between Los Angeles and Tokyo (0.961). The overall darker colors indicate a larger difference between these two cities. Upon closer inspection, slight differences can be observed between panels (f, g), which can be attributed to inherent errors in the algorithm. Maps a, b, c, e, f, and g are copyrighted by OpenStreetMap contributors.
