# Revisiting Graph Contrastive Learning from the Perspective of Graph Spectrum

arXiv: https://arxiv.org/abs/2210.02330 · HTML: https://mlsanity.com/paper/2210.02330/

## Key facts

- Cited by 43 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 48 references that are in the map.
- First posted on arXiv 5 Oct 2022.

## Builds on (most cited first, 23 of 23)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [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)
- [Strategies for Pre-training Graph Neural Networks](https://mlsanity.com/paper/1905.12265/) (2019)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Contrastive Multi-View Representation Learning on Graphs](https://mlsanity.com/paper/2006.05582/) (2020)
- [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)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [Point-GNN: Graph Neural Network for 3D Object Detection in a Point Cloud](https://mlsanity.com/paper/2003.01251/) (2020)
- [Revisiting Graph Neural Networks: All We Have is Low-Pass Filters](https://mlsanity.com/paper/1905.09550/) (2019)
- [Adversarial Graph Augmentation to Improve Graph Contrastive Learning](https://mlsanity.com/paper/2106.05819/) (2021)
- [From Canonical Correlation Analysis to Self-supervised Graph Neural Networks](https://mlsanity.com/paper/2106.12484/) (2021)
- [InfoGCL: Information-Aware Graph Contrastive Learning](https://mlsanity.com/paper/2110.15438/) (2021)
- [Augmentation-Free Self-Supervised Learning on Graphs](https://mlsanity.com/paper/2112.02472/) (2021)

## Built on by (most cited first, 30 of 43)

- [Position: Graph Foundation Models are Already Here](https://mlsanity.com/paper/2402.02216/) (2024)
- [Text-space Graph Foundation Models: Comprehensive Benchmarks and New Insights](https://mlsanity.com/paper/2406.10727/) (2024)
- [Simple and Asymmetric Graph Contrastive Learning without Augmentations](https://mlsanity.com/paper/2310.18884/) (2023)
- [Revisiting Multimodal Emotion Recognition in Conversation from the Perspective of Graph Spectrum](https://mlsanity.com/paper/2404.17862/) (2024)
- [A Survey on Spectral Graph Neural Networks](https://mlsanity.com/paper/2302.05631/) (2023)
- [Data-centric Graph Learning: A Survey](https://mlsanity.com/paper/2310.04987/) (2023)
- [SpeGCL: Self-supervised Graph Spectrum Contrastive Learning without Positive Samples](https://mlsanity.com/paper/2410.10365/) (2024)
- [Single-Pass Contrastive Learning Can Work for Both Homophilic and Heterophilic Graph](https://mlsanity.com/paper/2211.10890/) (2022)
- [Unveiling Vulnerabilities of Contrastive Recommender Systems to Poisoning Attacks](https://mlsanity.com/paper/2311.18244/) (2023)
- [LLM-Empowered Class Imbalanced Graph Prompt Learning for Online Drug Trafficking Detection](https://mlsanity.com/paper/2503.01900/) (2025)
- [Multimodal Emotion Recognition in Conversations: A Survey of Methods, Trends, Challenges and Prospects](https://mlsanity.com/paper/2505.20511/) (2025)
- [Localized Contrastive Learning on Graphs](https://mlsanity.com/paper/2212.04604/) (2022)
- [A Survey on Self-Supervised Graph Foundation Models: Knowledge-Based Perspective](https://mlsanity.com/paper/2403.16137/) (2024)
- [Self-Pro: A Self-Prompt and Tuning Framework for Graph Neural Networks](https://mlsanity.com/paper/2310.10362/) (2023)
- [GraphAgent: Agentic Graph Language Assistant](https://mlsanity.com/paper/2412.17029/) (2024)
- [Architecture Matters: Uncovering Implicit Mechanisms in Graph Contrastive Learning](https://mlsanity.com/paper/2311.02687/) (2023)
- [Revisiting Self-Supervised Heterogeneous Graph Learning from Spectral Clustering Perspective](https://mlsanity.com/paper/2412.00742/) (2024)
- [S2FGL: Spatial Spectral Federated Graph Learning](https://mlsanity.com/paper/2507.02409/) (2025)
- [Shape-aware Graph Spectral Learning](https://mlsanity.com/paper/2310.10064/) (2023)
- [Graph Contrastive Learning with Cohesive Subgraph Awareness](https://mlsanity.com/paper/2401.17580/) (2024)
- [Graph Contrastive Learning under Heterophily via Graph Filters](https://mlsanity.com/paper/2303.06344/) (2023)
- [Community-Invariant Graph Contrastive Learning](https://mlsanity.com/paper/2405.01350/) (2024)
- [Perfect Alignment May be Poisonous to Graph Contrastive Learning](https://mlsanity.com/paper/2310.03977/) (2023)
- [Efficient Model-Stealing Attacks Against Inductive Graph Neural Networks](https://mlsanity.com/paper/2405.12295/) (2024)
- [Through the Dual-Prism: A Spectral Perspective on Graph Data Augmentation for Graph Classification](https://mlsanity.com/paper/2401.09953/) (2024)
- [Principled Data Augmentation for Learning to Solve Quadratic Programming Problems](https://mlsanity.com/paper/2506.01728/) (2025)
- [Rethinking Spectral Augmentation for Contrast-based Graph Self-Supervised Learning](https://mlsanity.com/paper/2405.19600/) (2024)
- [AS-GCL: Asymmetric Spectral Augmentation on Graph Contrastive Learning](https://mlsanity.com/paper/2502.13525/) (2025)
- [Hodge-Aware Contrastive Learning](https://mlsanity.com/paper/2309.07364/) (2023)
- [Uncertainty in Graph Contrastive Learning with Bayesian Neural Networks](https://mlsanity.com/paper/2312.00232/) (2023)

## Abstract (arXiv)

Graph Contrastive Learning (GCL), learning the node representations by augmenting graphs, has attracted considerable attentions. Despite the proliferation of various graph augmentation strategies, some fundamental questions still remain unclear: what information is essentially encoded into the learned representations by GCL? Are there some general graph augmentation rules behind different augmentations? If so, what are they and what insights can they bring? In this paper, we answer these questions by establishing the connection between GCL and graph spectrum. By an experimental investigation in spectral domain, we firstly find the General grAph augMEntation (GAME) rule for GCL, i.e., the difference of the high-frequency parts between two augmented graphs should be larger than that of low-frequency parts. This rule reveals the fundamental principle to revisit the current graph augmentations and design new effective graph augmentations. Then we theoretically prove that GCL is able to learn the invariance information by contrastive invariance theorem, together with our GAME rule, for the first time, we uncover that the learned representations by GCL essentially encode the low-frequency information, which explains why GCL works. Guided by this rule, we propose a spectral graph contrastive learning module (SpCo), which is a general and GCL-friendly plug-in. We combine it with different existing GCL models, and extensive experiments well demonstrate that it can further improve the performances of a wide variety of different GCL methods.