# ES-GNN: Generalizing Graph Neural Networks Beyond Homophily with Edge Splitting

arXiv: https://arxiv.org/abs/2205.13700 · HTML: https://mlsanity.com/paper/2205.13700/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 67 of its 123 references that are in the map.
- First posted on arXiv 27 May 2022.

## Builds on (most cited first, 30 of 67)

- [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)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Graph Convolutional Neural Networks for Web-Scale Recommender Systems](https://mlsanity.com/paper/1806.01973/) (2018)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [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)
- [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)
- [Deep Learning on Graphs: A Survey](https://mlsanity.com/paper/1812.04202/) (2018)
- [Graph Structure Learning for Robust Graph Neural Networks](https://mlsanity.com/paper/2005.10203/) (2020)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [Improving Graph Neural Network Expressivity via Subgraph Isomorphism Counting](https://mlsanity.com/paper/2006.09252/) (2020)
- [Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methods](https://mlsanity.com/paper/2110.14446/) (2021)
- [Towards a Definition of Disentangled Representations](https://mlsanity.com/paper/1812.02230/) (2018)
- [Revisiting Graph Neural Networks: All We Have is Low-Pass Filters](https://mlsanity.com/paper/1905.09550/) (2019)
- [Learning to Represent Programs with Graphs](https://mlsanity.com/paper/1711.00740/) (2017)
- [Graph Neural Networks with Heterophily](https://mlsanity.com/paper/2009.13566/) (2020)
- [Graph Neural Networks with convolutional ARMA filters](https://mlsanity.com/paper/1901.01343/) (2019)
- [Two Sides of the Same Coin: Heterophily and Oversmoothing in Graph Convolutional Neural Networks](https://mlsanity.com/paper/2102.06462/) (2021)
- [Is Homophily a Necessity for Graph Neural Networks?](https://mlsanity.com/paper/2106.06134/) (2021)
- [Finding Global Homophily in Graph Neural Networks When Meeting Heterophily](https://mlsanity.com/paper/2205.07308/) (2022)
- [Interpretable and Generalizable Graph Learning via Stochastic Attention Mechanism](https://mlsanity.com/paper/2201.12987/) (2022)

## Built on by (most cited first, 13 of 13)

- [The Heterophilic Graph Learning Handbook: Benchmarks, Models, Theoretical Analysis, Applications and Challenges](https://mlsanity.com/paper/2407.09618/) (2024)
- [Graph Neural Networks with Diverse Spectral Filtering](https://mlsanity.com/paper/2312.09041/) (2023)
- [Preventing Representational Rank Collapse in MPNNs by Splitting the Computational Graph](https://mlsanity.com/paper/2409.11504/) (2024)
- [Navigating Distribution Shifts in Medical Image Analysis: A Survey](https://mlsanity.com/paper/2411.05824/) (2024)
- [Beyond Fixed Depth: Adaptive Graph Neural Networks for Node Classification Under Varying Homophily](https://mlsanity.com/paper/2511.06608/) (2025)
- [Rethinking Spectral Graph Neural Networks with Spatially Adaptive Filtering](https://mlsanity.com/paper/2401.09071/) (2024)
- [Edge-Splitting MLP: Node Classification on Homophilic and Heterophilic Graphs without Message Passing](https://mlsanity.com/paper/2412.08310/) (2024)
- [Jensen-Shannon Divergence Message-Passing for Rich-Text Graph Representation Learning](https://mlsanity.com/paper/2512.20094/) (2025)
- [HyperAggregation: Aggregating over Graph Edges with Hypernetworks](https://mlsanity.com/paper/2407.11596/) (2024)
- [A Generative Graph Contrastive Learning Model with Global Signal](https://mlsanity.com/paper/2504.18148/) (2025)
- [Bridging Computational Social Science and Deep Learning: Cultural Dissemination-Inspired Graph Neural Networks](https://mlsanity.com/paper/2509.19084/) (2025)
- [Efficient and Scalable Granular-ball Graph Coarsening Method for Large-scale Graph Node Classification](https://mlsanity.com/paper/2603.29148/) (2026)
- [Grad2Fair: A Gradient-driven Approach for Graph Fairness without Demographics](https://mlsanity.com/paper/2607.14705/) (2026)

## Abstract (arXiv)

While Graph Neural Networks (GNNs) have achieved enormous success in multiple graph analytical tasks, modern variants mostly rely on the strong inductive bias of homophily. However, real-world networks typically exhibit both homophilic and heterophilic linking patterns, wherein adjacent nodes may share dissimilar attributes and distinct labels. Therefore, GNNs smoothing node proximity holistically may aggregate both task-relevant and irrelevant (even harmful) information, limiting their ability to generalize to heterophilic graphs and potentially causing non-robustness. In this work, we propose a novel Edge Splitting GNN (ES-GNN) framework to adaptively distinguish between graph edges either relevant or irrelevant to learning tasks. This essentially transfers the original graph into two subgraphs with the same node set but complementary edge sets dynamically. Given that, information propagation separately on these subgraphs and edge splitting are alternatively conducted, thus disentangling the task-relevant and irrelevant features. Theoretically, we show that our ES-GNN can be regarded as a solution to a disentangled graph denoising problem, which further illustrates our motivations and interprets the improved generalization beyond homophily. Extensive experiments over 11 benchmark and 1 synthetic datasets not only demonstrate the effective performance of ES-GNN but also highlight its robustness to adversarial graphs and mitigation of the over-smoothing problem.