# Beyond Smoothing: Unsupervised Graph Representation Learning with Edge Heterophily Discriminating

arXiv: https://arxiv.org/abs/2211.14065 · HTML: https://mlsanity.com/paper/2211.14065/

## Key facts

- Cited by 57 papers in the map (data through 14 Oct 2026).
- Builds on 57 of its 80 references that are in the map.
- First posted on arXiv 25 Nov 2022.

## Builds on (most cited first, 30 of 57)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Contrastive Multi-View Representation Learning on Graphs](https://mlsanity.com/paper/2006.05582/) (2020)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [LINE: Large-scale Information Network Embedding](https://mlsanity.com/paper/1503.03578/) (2015)
- [Deep Graph Contrastive Representation Learning](https://mlsanity.com/paper/2006.04131/) (2020)
- [Graph Contrastive Learning with Adaptive Augmentation](https://mlsanity.com/paper/2010.14945/) (2020)
- [GCC: Graph Contrastive Coding for Graph Neural Network Pre-Training](https://mlsanity.com/paper/2006.09963/) (2020)
- [FedProto: Federated Prototype Learning across Heterogeneous Clients](https://mlsanity.com/paper/2105.00243/) (2021)
- [Graph Neural Networks with Learnable Structural and Positional Representations](https://mlsanity.com/paper/2110.07875/) (2021)
- [Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methods](https://mlsanity.com/paper/2110.14446/) (2021)
- [Graph Self-Supervised Learning: A Survey](https://mlsanity.com/paper/2103.00111/) (2021)

## Built on by (most cited first, 30 of 57)

- [Structure-free Graph Condensation: From Large-scale Graphs to Condensed Graph-free Data](https://mlsanity.com/paper/2306.02664/) (2023)
- [ARC: A Generalist Graph Anomaly Detector with In-Context Learning](https://mlsanity.com/paper/2405.16771/) (2024)
- [Truncated Affinity Maximization: One-class Homophily Modeling for Graph Anomaly Detection](https://mlsanity.com/paper/2306.00006/) (2023)
- [Towards Self-Interpretable Graph-Level Anomaly Detection](https://mlsanity.com/paper/2310.16520/) (2023)
- [Dink-Net: Neural Clustering on Large Graphs](https://mlsanity.com/paper/2305.18405/) (2023)
- [Federated Graph Semantic and Structural Learning](https://mlsanity.com/paper/2406.18937/) (2024)
- [Learning Strong Graph Neural Networks with Weak Information](https://mlsanity.com/paper/2305.18457/) (2023)
- [Finding the Missing-half: Graph Complementary Learning for Homophily-prone and Heterophily-prone Graphs](https://mlsanity.com/paper/2306.07608/) (2023)
- [PREM: A Simple Yet Effective Approach for Node-Level Graph Anomaly Detection](https://mlsanity.com/paper/2310.11676/) (2023)
- [Auto-HeG: Automated Graph Neural Network on Heterophilic Graphs](https://mlsanity.com/paper/2302.12357/) (2023)
- [Data-centric Graph Learning: A Survey](https://mlsanity.com/paper/2310.04987/) (2023)
- [Normalizing Flow-based Neural Process for Few-Shot Knowledge Graph Completion](https://mlsanity.com/paper/2304.08183/) (2023)
- [Oversmoothing, Oversquashing, Heterophily, Long-Range, and more: Demystifying Common Beliefs in Graph Machine Learning](https://mlsanity.com/paper/2505.15547/) (2025)
- [GNNEvaluator: Evaluating GNN Performance On Unseen Graphs Without Labels](https://mlsanity.com/paper/2310.14586/) (2023)
- [Learn Beneficial Noise as Graph Augmentation](https://mlsanity.com/paper/2505.19024/) (2025)
- [MUSE: Multi-View Contrastive Learning for Heterophilic Graphs](https://mlsanity.com/paper/2307.16026/) (2023)
- [Online GNN Evaluation Under Test-time Graph Distribution Shifts](https://mlsanity.com/paper/2403.09953/) (2024)
- [When Heterophily Meets Heterogeneous Graphs: Latent Graphs Guided Unsupervised Representation Learning](https://mlsanity.com/paper/2409.00687/) (2024)
- [CVTGAD: Simplified Transformer with Cross-View Attention for Unsupervised Graph-level Anomaly Detection](https://mlsanity.com/paper/2405.02359/) (2024)
- [A Survey on Self-Supervised Graph Foundation Models: Knowledge-Based Perspective](https://mlsanity.com/paper/2403.16137/) (2024)
- [Homophily-Related: Adaptive Hybrid Graph Filter for Multi-View Graph Clustering](https://mlsanity.com/paper/2401.02682/) (2024)
- [Graph Contrastive Learning under Heterophily via Graph Filters](https://mlsanity.com/paper/2303.06344/) (2023)
- [HC-GLAD: Dual Hyperbolic Contrastive Learning for Unsupervised Graph-Level Anomaly Detection](https://mlsanity.com/paper/2407.02057/) (2024)
- [Refining Latent Homophilic Structures over Heterophilic Graphs for Robust Graph Convolution Networks](https://mlsanity.com/paper/2312.16418/) (2023)
- [Noisy Node Classification by Bi-level Optimization based Multi-teacher Distillation](https://mlsanity.com/paper/2404.17875/) (2024)
- [Heterophilic Graph Neural Networks Optimization with Causal Message-passing](https://mlsanity.com/paper/2411.13821/) (2024)
- [Discrepancy-Aware Graph Mask Auto-Encoder](https://mlsanity.com/paper/2506.19343/) (2025)
- [GPatcher: A Simple and Adaptive MLP Model for Alleviating Graph Heterophily](https://mlsanity.com/paper/2306.14340/) (2023)
- [VeTraSS: Vehicle Trajectory Similarity Search Through Graph Modeling and Representation Learning](https://mlsanity.com/paper/2404.08021/) (2024)
- [Str-GCL: Structural Commonsense Driven Graph Contrastive Learning](https://mlsanity.com/paper/2507.07141/) (2025)

## Abstract (arXiv)

Unsupervised graph representation learning (UGRL) has drawn increasing research attention and achieved promising results in several graph analytic tasks. Relying on the homophily assumption, existing UGRL methods tend to smooth the learned node representations along all edges, ignoring the existence of heterophilic edges that connect nodes with distinct attributes. As a result, current methods are hard to generalize to heterophilic graphs where dissimilar nodes are widely connected, and also vulnerable to adversarial attacks. To address this issue, we propose a novel unsupervised Graph Representation learning method with Edge hEterophily discriminaTing (GREET) which learns representations by discriminating and leveraging homophilic edges and heterophilic edges. To distinguish two types of edges, we build an edge discriminator that infers edge homophily/heterophily from feature and structure information. We train the edge discriminator in an unsupervised way through minimizing the crafted pivot-anchored ranking loss, with randomly sampled node pairs acting as pivots. Node representations are learned through contrasting the dual-channel encodings obtained from the discriminated homophilic and heterophilic edges. With an effective interplaying scheme, edge discriminating and representation learning can mutually boost each other during the training phase. We conducted extensive experiments on 14 benchmark datasets and multiple learning scenarios to demonstrate the superiority of GREET.