ABSTRACT 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

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. Access through your institution Buy or subscribe This is a preview of subscription content, access via your institution ACCESS

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Read our FAQs * Contact customer support SIMILAR CONTENT BEING VIEWED BY OTHERS URBANITY: AUTOMATED MODELLING AND ANALYSIS OF MULTIDIMENSIONAL NETWORKS IN CITIES Article Open access 25 July

2023 NEURAL EMBEDDINGS OF URBAN BIG DATA REVEAL SPATIAL STRUCTURES IN CITIES Article Open access 14 March 2024 QUANTIFYING THE NON-ISOMORPHISM OF GLOBAL URBAN ROAD NETWORKS USING GNNS AND

GRAPH KERNELS Article Open access 22 February 2025 DATA AVAILABILITY We used the publicly available road network data from OpenStreetMap (https://www.openstreetmap.org/) via the OSMnx Python

package (https://github.com/gboeing/osmnx). We also used images from Google Maps (https://www.google.com/maps) to validate the node merging results. These images are also available to the

public. The population data we used comes from https://worldpopulationreview.com/, which is a visualization platform for the open datasets owned by the United Nations. The airport flow data

for 21 cities are from the 2019 Annual Airport Traffic Report at https://www.panynj.gov/airports/en/statistics-general-info.html owned by the Port Authority of New York and New Jersey and

are also publicly available. The airport flow data for the other nine cities can be accessed from links that are listed in Supplementary Section 4. Both the road network data and

socioeconomic data are available at the online data warehouse: https://github.com/jiang719/road-network-predictability.git. The data are available via Zenodo at

https://doi.org/10.5281/zenodo.5866593 (ref. 109). CODE AVAILABILITY Source codes for the training and testing results are available at the online data warehouse:

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networks via graph neural networks [Data set]. _Zenodo_ https://doi.org/10.5281/zenodo.5866593 (2022). Download references ACKNOWLEDGEMENTS We thank S. Rao from Purdue University for

discussions about the comparison between the spatial homogeneity metric and existing network metrics. S.L. acknowledges support from the Ross-Lynn fellowship, Purdue University. T.Y. is

partly funded by National Science Foundation (grant number 1638311). AUTHOR INFORMATION AUTHORS AND AFFILIATIONS * Lyles School of Civil Engineering, Purdue University, West Lafayette, IN,

USA Jiawei Xue, Takahiro Yabe & Satish V. Ukkusuri * Department of Computer Science, Purdue University, West Lafayette, IN, USA Nan Jiang & Jianzhu Ma * Department of Mathematics,

Purdue University, West Lafayette, IN, USA Senwei Liang & Qiyuan Pang * Institute for Artificial Intelligence, Peking University, Beijing, China Jianzhu Ma * Beijing Institute for

General Artificial Intelligence, Beijing, China Jianzhu Ma Authors * Jiawei Xue View author publications You can also search for this author inPubMed Google Scholar * Nan Jiang View author

publications You can also search for this author inPubMed Google Scholar * Senwei Liang View author publications You can also search for this author inPubMed Google Scholar * Qiyuan Pang

View author publications You can also search for this author inPubMed Google Scholar * Takahiro Yabe View author publications You can also search for this author inPubMed Google Scholar *

Satish V. Ukkusuri View author publications You can also search for this author inPubMed Google Scholar * Jianzhu Ma View author publications You can also search for this author inPubMed 

Google Scholar CONTRIBUTIONS J.X., T.Y., S.V.U. and J.M. proposed the question. J.X., N.J., S.L., Q.P. and J.M. designed the research. N.J. trained and tested the GNN models. S.L. and Q.P.

performed the intracity analysis. N.J. and J.X. conducted the intercity analysis. J.X. and J.M. drew the figures. J.X., T.Y., S.V.U. and J.M. wrote the paper. CORRESPONDING AUTHORS

Correspondence to Satish V. Ukkusuri or Jianzhu Ma. ETHICS DECLARATIONS COMPETING INTERESTS The authors declare no competing interests. PEER REVIEW PEER REVIEW INFORMATION _Nature Machine

Intelligence_ thanks Martin Fleischmann and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. ADDITIONAL INFORMATION PUBLISHER’S NOTE Springer Nature

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1–5. REPORTING SUMMARY RIGHTS AND PERMISSIONS Reprints and permissions ABOUT THIS ARTICLE CITE THIS ARTICLE Xue, J., Jiang, N., Liang, S. _et al._ Quantifying the spatial homogeneity of

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