# A Survey on Graph Structure Learning: Progress and Opportunities

arXiv: https://arxiv.org/abs/2103.03036 · HTML: https://mlsanity.com/paper/2103.03036/

## Key facts

- Cited by 71 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 52 references that are in the map.
- First posted on arXiv 4 Mar 2021.

## Builds on (most cited first, 24 of 24)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [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)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [A Generalization of Transformer Networks to Graphs](https://mlsanity.com/paper/2012.09699/) (2020)
- [Learning Sparse Neural Networks through L0 Regularization](https://mlsanity.com/paper/1712.01312/) (2017)
- [Graph Contrastive Learning with Adaptive Augmentation](https://mlsanity.com/paper/2010.14945/) (2020)
- [Parameterized Explainer for Graph Neural Network](https://mlsanity.com/paper/2011.04573/) (2020)
- [Diffusion Improves Graph Learning](https://mlsanity.com/paper/1911.05485/) (2019)
- [Graph Structure Learning for Robust Graph Neural Networks](https://mlsanity.com/paper/2005.10203/) (2020)
- [Adversarial Attack on Graph Structured Data](https://mlsanity.com/paper/1806.02371/) (2018)
- [Learning Discrete Structures for Graph Neural Networks](https://mlsanity.com/paper/1903.11960/) (2019)
- [Iterative Deep Graph Learning for Graph Neural Networks: Better and Robust Node Embeddings](https://mlsanity.com/paper/2006.13009/) (2020)
- [Adaptive Graph Convolutional Neural Networks](https://mlsanity.com/paper/1801.03226/) (2018)
- [How to learn a graph from smooth signals](https://mlsanity.com/paper/1601.02513/) (2016)
- [Learning to Drop: Robust Graph Neural Network via Topological Denoising](https://mlsanity.com/paper/2011.07057/) (2020)
- [Learning graphs from data: A signal representation perspective](https://mlsanity.com/paper/1806.00848/) (2018)
- [SLAPS: Self-Supervision Improves Structure Learning for Graph Neural Networks](https://mlsanity.com/paper/2102.05034/) (2021)
- [Generating Classification Weights with GNN Denoising Autoencoders for Few-Shot Learning](https://mlsanity.com/paper/1905.01102/) (2019)
- [Attention Models in Graphs: A Survey](https://mlsanity.com/paper/1807.07984/) (2018)
- [Graph Representation Learning via Hard and Channel-Wise Attention Networks](https://mlsanity.com/paper/1907.04652/) (2019)
- [CAGNN: Cluster-Aware Graph Neural Networks for Unsupervised Graph Representation Learning](https://mlsanity.com/paper/2009.01674/) (2020)
- [Class-Attentive Diffusion Network for Semi-Supervised Classification](https://mlsanity.com/paper/2006.10222/) (2020)

## Built on by (most cited first, 30 of 71)

- [DiffWire: Inductive Graph Rewiring via the Lov'asz Bound](https://mlsanity.com/paper/2206.07369/) (2022)
- [A Survey on Deep Graph Generation: Methods and Applications](https://mlsanity.com/paper/2203.06714/) (2022)
- [MolGenSurvey: A Systematic Survey in Machine Learning Models for Molecule Design](https://mlsanity.com/paper/2203.14500/) (2022)
- [Graph Data Augmentation for Graph Machine Learning: A Survey](https://mlsanity.com/paper/2202.08871/) (2022)
- [A Comprehensive Survey on Graph Reduction: Sparsification, Coarsening, and Condensation](https://mlsanity.com/paper/2402.03358/) (2024)
- [GSLB: The Graph Structure Learning Benchmark](https://mlsanity.com/paper/2310.05174/) (2023)
- [Towards Understanding the Generalization of Graph Neural Networks](https://mlsanity.com/paper/2305.08048/) (2023)
- [A Comprehensive Survey on Data Augmentation](https://mlsanity.com/paper/2405.09591/) (2024)
- [T2-GNN: Graph Neural Networks for Graphs with Incomplete Features and Structure via Teacher-Student Distillation](https://mlsanity.com/paper/2212.12738/) (2022)
- [Modeling Multivariate Biosignals With Graph Neural Networks and Structured State Space Models](https://mlsanity.com/paper/2211.11176/) (2022)
- [The Heterophilic Graph Learning Handbook: Benchmarks, Models, Theoretical Analysis, Applications and Challenges](https://mlsanity.com/paper/2407.09618/) (2024)
- [Make Heterophily Graphs Better Fit GNN: A Graph Rewiring Approach](https://mlsanity.com/paper/2209.08264/) (2022)
- [Data-centric Graph Learning: A Survey](https://mlsanity.com/paper/2310.04987/) (2023)
- [Comprehensive Graph Gradual Pruning for Sparse Training in Graph Neural Networks](https://mlsanity.com/paper/2207.08629/) (2022)
- [Graph Anomaly Detection in Time Series: A Survey](https://mlsanity.com/paper/2302.00058/) (2023)
- [DSLR: Diversity Enhancement and Structure Learning for Rehearsal-based Graph Continual Learning](https://mlsanity.com/paper/2402.13711/) (2024)
- [CTINexus: Automatic Cyber Threat Intelligence Knowledge Graph Construction Using Large Language Models](https://mlsanity.com/paper/2410.21060/) (2024)
- [Graph-Augmented Large Language Model Agents: Current Progress and Future Prospects](https://mlsanity.com/paper/2507.21407/) (2025)
- [Molecular Property Prediction Based on Graph Structure Learning](https://mlsanity.com/paper/2312.16855/) (2023)
- [Graph Neural Networks for Tabular Data Learning: A Survey with Taxonomy and Directions](https://mlsanity.com/paper/2401.02143/) (2024)
- [Graph Neural Networks for Brain Graph Learning: A Survey](https://mlsanity.com/paper/2406.02594/) (2024)
- [Graph Neural Networks in Histopathology: Emerging Trends and Future Directions](https://mlsanity.com/paper/2406.12808/) (2024)
- [Toward Robust Graph Semi-Supervised Learning against Extreme Data Scarcity](https://mlsanity.com/paper/2208.12422/) (2022)
- [Graph Convolution Based Efficient Re-Ranking for Visual Retrieval](https://mlsanity.com/paper/2306.08792/) (2023)
- [Spatio-Temporal Dynamic Graph Relation Learning for Urban Metro Flow Prediction](https://mlsanity.com/paper/2204.02650/) (2022)
- [Curb Your Attention: Causal Attention Gating for Robust Trajectory Prediction in Autonomous Driving](https://mlsanity.com/paper/2410.07191/) (2024)
- [STG4Traffic: A Survey and Benchmark of Spatial-Temporal Graph Neural Networks for Traffic Prediction](https://mlsanity.com/paper/2307.00495/) (2023)
- [DGDNN: Decoupled Graph Diffusion Neural Network for Stock Movement Prediction](https://mlsanity.com/paper/2401.01846/) (2024)
- [Adversarially Robust Neural Architecture Search for Graph Neural Networks](https://mlsanity.com/paper/2304.04168/) (2023)
- [Learning Time-aware Graph Structures for Spatially Correlated Time Series Forecasting](https://mlsanity.com/paper/2312.16403/) (2023)

## Abstract (arXiv)

Graphs are widely used to describe real-world objects and their interactions. Graph Neural Networks (GNNs) as a de facto model for analyzing graphstructured data, are highly sensitive to the quality of the given graph structures. Therefore, noisy or incomplete graphs often lead to unsatisfactory representations and prevent us from fully understanding the mechanism underlying the system. In pursuit of an optimal graph structure for downstream tasks, recent studies have sparked an effort around the central theme of Graph Structure Learning (GSL), which aims to jointly learn an optimized graph structure and corresponding graph representations. In the presented survey, we broadly review recent progress in GSL methods. Specifically, we first formulate a general pipeline of GSL and review state-of-the-art methods classified by the way of modeling graph structures, followed by applications of GSL across domains. Finally, we point out some issues in current studies and discuss future directions.