# New Benchmarks for Learning on Non-Homophilous Graphs

arXiv: https://arxiv.org/abs/2104.01404 · HTML: https://mlsanity.com/paper/2104.01404/

## Key facts

- Cited by 81 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 67 references that are in the map.
- First posted on arXiv 3 Apr 2021.

## Builds on (most cited first, 30 of 35)

- [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)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [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)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [Diffusion Improves Graph Learning](https://mlsanity.com/paper/1911.05485/) (2019)
- [Community Detection and Stochastic Block Models](https://mlsanity.com/paper/1703.10146/) (2017)
- [Revisiting Graph Neural Networks: All We Have is Low-Pass Filters](https://mlsanity.com/paper/1905.09550/) (2019)
- [Enhancing Graph Neural Network-based Fraud Detectors against Camouflaged Fraudsters](https://mlsanity.com/paper/2008.08692/) (2020)
- [Graph Neural Networks with Heterophily](https://mlsanity.com/paper/2009.13566/) (2020)
- [Combining Label Propagation and Simple Models Out-performs Graph Neural Networks](https://mlsanity.com/paper/2010.13993/) (2020)
- [Two Sides of the Same Coin: Heterophily and Oversmoothing in Graph Convolutional Neural Networks](https://mlsanity.com/paper/2102.06462/) (2021)
- [Scaling Graph Neural Networks with Approximate PageRank](https://mlsanity.com/paper/2007.01570/) (2020)
- [Contextual Stochastic Block Models](https://mlsanity.com/paper/1807.09596/) (2018)
- [Characteristic Functions on Graphs: Birds of a Feather, from Statistical Descriptors to Parametric Models](https://mlsanity.com/paper/2005.07959/) (2020)

## Built on by (most cited first, 30 of 81)

- [Long Range Graph Benchmark](https://mlsanity.com/paper/2206.08164/) (2022)
- [NodeFormer: A Scalable Graph Structure Learning Transformer for Node Classification](https://mlsanity.com/paper/2306.08385/) (2023)
- [Graph Neural Networks for Graphs with Heterophily: A Survey](https://mlsanity.com/paper/2202.07082/) (2022)
- [Revisiting Heterophily For Graph Neural Networks](https://mlsanity.com/paper/2210.07606/) (2022)
- [Handling Distribution Shifts on Graphs: An Invariance Perspective](https://mlsanity.com/paper/2202.02466/) (2022)
- [Graph-less Neural Networks: Teaching Old MLPs New Tricks via Distillation](https://mlsanity.com/paper/2110.08727/) (2021)
- [Node Feature Extraction by Self-Supervised Multi-scale Neighborhood Prediction](https://mlsanity.com/paper/2111.00064/) (2021)
- [SGFormer: Simplifying and Empowering Transformers for Large-Graph Representations](https://mlsanity.com/paper/2306.10759/) (2023)
- [You are AllSet: A Multiset Function Framework for Hypergraph Neural Networks](https://mlsanity.com/paper/2106.13264/) (2021)
- [Is Heterophily A Real Nightmare For Graph Neural Networks To Do Node Classification?](https://mlsanity.com/paper/2109.05641/) (2021)
- [Empowering Graph Representation Learning with Test-Time Graph Transformation](https://mlsanity.com/paper/2210.03561/) (2022)
- [Ordered GNN: Ordering Message Passing to Deal with Heterophily and Over-smoothing](https://mlsanity.com/paper/2302.01524/) (2023)
- [Certified Graph Unlearning](https://mlsanity.com/paper/2206.09140/) (2022)
- [Beyond Homophily: Reconstructing Structure for Graph-agnostic Clustering](https://mlsanity.com/paper/2305.02931/) (2023)
- [The Heterophilic Graph Learning Handbook: Benchmarks, Models, Theoretical Analysis, Applications and Challenges](https://mlsanity.com/paper/2407.09618/) (2024)
- [Towards Deep Attention in Graph Neural Networks: Problems and Remedies](https://mlsanity.com/paper/2306.02376/) (2023)
- [Beyond Real-world Benchmark Datasets: An Empirical Study of Node Classification with GNNs](https://mlsanity.com/paper/2206.09144/) (2022)
- [Make Heterophily Graphs Better Fit GNN: A Graph Rewiring Approach](https://mlsanity.com/paper/2209.08264/) (2022)
- [Partitioning Message Passing for Graph Fraud Detection](https://mlsanity.com/paper/2412.00020/) (2024)
- [Node-oriented Spectral Filtering for Graph Neural Networks](https://mlsanity.com/paper/2212.03654/) (2022)
- [Node-wise Filtering in Graph Neural Networks: A Mixture of Experts Approach](https://mlsanity.com/paper/2406.03464/) (2024)
- [Lorentzian Residual Neural Networks](https://mlsanity.com/paper/2412.14695/) (2024)
- [Augmentation-Free Graph Contrastive Learning with Performance Guarantee](https://mlsanity.com/paper/2204.04874/) (2022)
- [Individual and Structural Graph Information Bottlenecks for Out-of-Distribution Generalization](https://mlsanity.com/paper/2306.15902/) (2023)
- [Feature Transportation Improves Graph Neural Networks](https://mlsanity.com/paper/2307.16092/) (2023)
- [Understanding Heterophily for Graph Neural Networks](https://mlsanity.com/paper/2401.09125/) (2024)
- [Beyond Low-pass Filtering: Graph Convolutional Networks with Automatic Filtering](https://mlsanity.com/paper/2107.04755/) (2021)
- [NOSMOG: Learning Noise-robust and Structure-aware MLPs on Graphs](https://mlsanity.com/paper/2208.10010/) (2022)
- [Single-Pass Contrastive Learning Can Work for Both Homophilic and Heterophilic Graph](https://mlsanity.com/paper/2211.10890/) (2022)
- [ES-GNN: Generalizing Graph Neural Networks Beyond Homophily with Edge Splitting](https://mlsanity.com/paper/2205.13700/) (2022)

## Abstract (arXiv)

Much data with graph structures satisfy the principle of homophily, meaning that connected nodes tend to be similar with respect to a specific attribute. As such, ubiquitous datasets for graph machine learning tasks have generally been highly homophilous, rewarding methods that leverage homophily as an inductive bias. Recent work has pointed out this particular focus, as new non-homophilous datasets have been introduced and graph representation learning models better suited for low-homophily settings have been developed. However, these datasets are small and poorly suited to truly testing the effectiveness of new methods in non-homophilous settings. We present a series of improved graph datasets with node label relationships that do not satisfy the homophily principle. Along with this, we introduce a new measure of the presence or absence of homophily that is better suited than existing measures in different regimes. We benchmark a range of simple methods and graph neural networks across our proposed datasets, drawing new insights for further research. Data and codes can be found at https://github.com/CUAI/Non-Homophily-Benchmarks.