# Quantifying Spatial Homogeneity of Urban Road Networks via Graph Neural Networks

arXiv: https://arxiv.org/abs/2101.00307 · HTML: https://mlsanity.com/paper/2101.00307/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 135 references that are in the map.
- First posted on arXiv 1 Jan 2021.

## Builds on (most cited first, 24 of 24)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Embedding Entities and Relations for Learning and Inference in Knowledge Bases](https://mlsanity.com/paper/1412.6575/) (2014)
- [Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View](https://mlsanity.com/paper/1909.03211/) (2019)
- [struc2vec: Learning Node Representations from Structural Identity](https://mlsanity.com/paper/1704.03165/) (2017)
- [Graph-Structured Representations for Visual Question Answering](https://mlsanity.com/paper/1609.05600/) (2016)
- [OSMnx: New Methods for Acquiring, Constructing, Analyzing, and Visualizing Complex Street Networks](https://mlsanity.com/paper/1611.01890/) (2016)
- [Simplicial Closure and higher-order link prediction](https://mlsanity.com/paper/1802.06916/) (2018)
- [Using Deep Learning and Google Street View to Estimate the Demographic Makeup of the US](https://mlsanity.com/paper/1702.06683/) (2017)
- [Learning from Multiple Cities: A Meta-Learning Approach for Spatial-Temporal Prediction](https://mlsanity.com/paper/1901.08518/) (2019)
- [Stacking Models for Nearly Optimal Link Prediction in Complex Networks](https://mlsanity.com/paper/1909.07578/) (2019)
- [Predicting commuter flows in spatial networks using a radiation model based on temporal ranges](https://mlsanity.com/paper/1410.4849/) (2014)
- [A simple contagion process describes spreading of traffic jams in urban networks](https://mlsanity.com/paper/1906.00585/) (2019)
- [Modelling urban networks using Variational Autoencoders](https://mlsanity.com/paper/1905.06465/) (2019)
- [Joint embedding of structure and features via graph convolutional networks](https://mlsanity.com/paper/1905.08636/) (2019)
- [Understanding metropolitan patterns of daily encounters](https://mlsanity.com/paper/1301.5979/) (2013)
- [A Multi-Scale Analysis of 27,000 Urban Street Networks: Every US City, Town, Urbanized Area, and Zillow Neighborhood](https://mlsanity.com/paper/1705.02198/) (2017)
- [Self-organization versus top-down planning in the evolution of a city](https://mlsanity.com/paper/1307.2203/) (2013)
- [Compressive Closeness in Networks](https://mlsanity.com/paper/1906.08335/) (2019)

## Built on by (most cited first, 8 of 8)

- [A Unified Framework for Combinatorial Optimization Based on Graph Neural Networks](https://mlsanity.com/paper/2406.13125/) (2024)
- [The maximum capability of a topological feature in link prediction](https://mlsanity.com/paper/2206.15101/) (2022)
- [Neural Embeddings of Urban Big Data Reveal Emergent Structures in Cities](https://mlsanity.com/paper/2110.12371/) (2021)
- [UrbanGraph: Physics-Informed Spatio-Temporal Dynamic Heterogeneous Graphs for Urban Microclimate Prediction](https://mlsanity.com/paper/2510.00457/) (2025)
- [Multi-Modal Feature Fusion for Spatial Morphology Analysis of Traditional Villages via Hierarchical Graph Neural Networks](https://mlsanity.com/paper/2510.27208/) (2025)
- [Collaborative Imputation of Urban Time Series through Cross-city Meta-learning](https://mlsanity.com/paper/2501.11306/) (2025)
- [Neighbor-aware informal settlement mapping with graph convolutional networks](https://mlsanity.com/paper/2509.26171/) (2025)
- [A Framework Based on Graph Cellular Automata for Similarity Evaluation in Urban Spatial Networks](https://mlsanity.com/paper/2511.00768/) (2025)

## Abstract (arXiv)

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.