# Spatial Heterophily Aware Graph Neural Networks

arXiv: https://arxiv.org/abs/2306.12139 · HTML: https://mlsanity.com/paper/2306.12139/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 56 references that are in the map.
- First posted on arXiv 21 Jun 2023.

## Builds on (most cited first, 30 of 34)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (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)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methods](https://mlsanity.com/paper/2110.14446/) (2021)
- [Spatial-Temporal Graph ODE Networks for Traffic Flow Forecasting](https://mlsanity.com/paper/2106.12931/) (2021)
- [Graph Neural Networks with Heterophily](https://mlsanity.com/paper/2009.13566/) (2020)
- [Two Sides of the Same Coin: Heterophily and Oversmoothing in Graph Convolutional Neural Networks](https://mlsanity.com/paper/2102.06462/) (2021)
- [Finding Global Homophily in Graph Neural Networks When Meeting Heterophily](https://mlsanity.com/paper/2205.07308/) (2022)
- [Node Similarity Preserving Graph Convolutional Networks](https://mlsanity.com/paper/2011.09643/) (2020)
- [How to Find Your Friendly Neighborhood: Graph Attention Design with Self-Supervision](https://mlsanity.com/paper/2204.04879/) (2022)
- [Breaking the Limit of Graph Neural Networks by Improving the Assortativity of Graphs with Local Mixing Patterns](https://mlsanity.com/paper/2106.06586/) (2021)
- [Non-Local Graph Neural Networks](https://mlsanity.com/paper/2005.14612/) (2020)
- [GBK-GNN: Gated Bi-Kernel Graph Neural Networks for Modeling Both Homophily and Heterophily](https://mlsanity.com/paper/2110.15777/) (2021)
- [Is Heterophily A Real Nightmare For Graph Neural Networks To Do Node Classification?](https://mlsanity.com/paper/2109.05641/) (2021)
- [New Benchmarks for Learning on Non-Homophilous Graphs](https://mlsanity.com/paper/2104.01404/) (2021)
- [Graph Neural Networks Inspired by Classical Iterative Algorithms](https://mlsanity.com/paper/2103.06064/) (2021)
- [Block Modeling-Guided Graph Convolutional Neural Networks](https://mlsanity.com/paper/2112.13507/) (2021)
- [Multi-Graph Fusion Networks for Urban Region Embedding](https://mlsanity.com/paper/2201.09760/) (2022)
- [Practical Adversarial Attacks on Spatiotemporal Traffic Forecasting Models](https://mlsanity.com/paper/2210.02447/) (2022)
- [Knowledge-infused Contrastive Learning for Urban Imagery-based Socioeconomic Prediction](https://mlsanity.com/paper/2302.13094/) (2023)
- [Event-Aware Multimodal Mobility Nowcasting](https://mlsanity.com/paper/2112.08443/) (2021)
- [Relational Fusion Networks: Graph Convolutional Networks for Road Networks](https://mlsanity.com/paper/2006.09030/) (2020)

## Built on by (most cited first, 7 of 7)

- [The Heterophilic Graph Learning Handbook: Benchmarks, Models, Theoretical Analysis, Applications and Challenges](https://mlsanity.com/paper/2407.09618/) (2024)
- [A Survey on Learning from Graphs with Heterophily: Recent Advances and Future Directions](https://mlsanity.com/paper/2401.09769/) (2024)
- [Conformal Load Prediction with Transductive Graph Autoencoders](https://mlsanity.com/paper/2406.08281/) (2024)
- [What Is Missing In Homophily? Disentangling Graph Homophily For Graph Neural Networks](https://mlsanity.com/paper/2406.18854/) (2024)
- [Structure-Enhanced Protein Instruction Tuning: Towards General-Purpose Protein Understanding with LLMs](https://mlsanity.com/paper/2410.03553/) (2024)
- [UrbanGraph: Physics-Informed Spatio-Temporal Dynamic Heterogeneous Graphs for Urban Microclimate Prediction](https://mlsanity.com/paper/2510.00457/) (2025)
- [MSRFormer: Road Network Representation Learning using Multi-scale Feature Fusion of Heterogeneous Spatial Interactions](https://mlsanity.com/paper/2509.05685/) (2025)

## Abstract (arXiv)

Graph Neural Networks (GNNs) have been broadly applied in many urban applications upon formulating a city as an urban graph whose nodes are urban objects like regions or points of interest. Recently, a few enhanced GNN architectures have been developed to tackle heterophily graphs where connected nodes are dissimilar. However, urban graphs usually can be observed to possess a unique spatial heterophily property; that is, the dissimilarity of neighbors at different spatial distances can exhibit great diversity. This property has not been explored, while it often exists. To this end, in this paper, we propose a metric, named Spatial Diversity Score, to quantitatively measure the spatial heterophily and show how it can influence the performance of GNNs. Indeed, our experimental investigation clearly shows that existing heterophilic GNNs are still deficient in handling the urban graph with high spatial diversity score. This, in turn, may degrade their effectiveness in urban applications. Along this line, we propose a Spatial Heterophily Aware Graph Neural Network (SHGNN), to tackle the spatial diversity of heterophily of urban graphs. Based on the key observation that spatially close neighbors on the urban graph present a more similar mode of difference to the central node, we first design a rotation-scaling spatial aggregation module, whose core idea is to properly group the spatially close neighbors and separately process each group with less diversity inside. Then, a heterophily-sensitive spatial interaction module is designed to adaptively capture the commonality and diverse dissimilarity in different spatial groups. Extensive experiments on three real-world urban datasets demonstrate the superiority of our SHGNN over several its competitors.