# SE-GSL: A General and Effective Graph Structure Learning Framework through Structural Entropy Optimization

arXiv: https://arxiv.org/abs/2303.09778 · HTML: https://mlsanity.com/paper/2303.09778/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 70 references that are in the map.
- First posted on arXiv 17 Mar 2023.

## Builds on (most cited first, 30 of 43)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [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)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (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)
- [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)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [GNNExplainer: Generating Explanations for Graph Neural Networks](https://mlsanity.com/paper/1903.03894/) (2019)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [Graph Contrastive Learning with Adaptive Augmentation](https://mlsanity.com/paper/2010.14945/) (2020)
- [Explaining Explanations: An Overview of Interpretability of Machine Learning](https://mlsanity.com/paper/1806.00069/) (2018)
- [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)
- [GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Models](https://mlsanity.com/paper/1802.08773/) (2018)
- [Graph Structure Learning for Robust Graph Neural Networks](https://mlsanity.com/paper/2005.10203/) (2020)
- [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)
- [Graph Random Neural Network for Semi-Supervised Learning on Graphs](https://mlsanity.com/paper/2005.11079/) (2020)
- [GraphLIME: Local Interpretable Model Explanations for Graph Neural Networks](https://mlsanity.com/paper/2001.06216/) (2020)
- [GNNGuard: Defending Graph Neural Networks against Adversarial Attacks](https://mlsanity.com/paper/2006.08149/) (2020)
- [Graph Information Bottleneck](https://mlsanity.com/paper/2010.12811/) (2020)
- [Adversarial Attack and Defense on Graph Data: A Survey](https://mlsanity.com/paper/1812.10528/) (2018)
- [Adaptive Graph Convolutional Neural Networks](https://mlsanity.com/paper/1801.03226/) (2018)
- [Learning to Drop: Robust Graph Neural Network via Topological Denoising](https://mlsanity.com/paper/2011.07057/) (2020)

## Built on by (most cited first, 30 of 35)

- [GraphEdit: Large Language Models for Graph Structure Learning](https://mlsanity.com/paper/2402.15183/) (2024)
- [OpenGSL: A Comprehensive Benchmark for Graph Structure Learning](https://mlsanity.com/paper/2306.10280/) (2023)
- [Probabilistically Rewired Message-Passing Neural Networks](https://mlsanity.com/paper/2310.02156/) (2023)
- [LSEnet: Lorentz Structural Entropy Neural Network for Deep Graph Clustering](https://mlsanity.com/paper/2405.11801/) (2024)
- [DeepRicci: Self-supervised Graph Structure-Feature Co-Refinement for Alleviating Over-squashing](https://mlsanity.com/paper/2401.12780/) (2024)
- [SeBot: Structural Entropy Guided Multi-View Contrastive Learning for Social Bot Detection](https://mlsanity.com/paper/2405.11225/) (2024)
- [Probabilistic Graph Rewiring via Virtual Nodes](https://mlsanity.com/paper/2405.17311/) (2024)
- [Hierarchical State Abstraction Based on Structural Information Principles](https://mlsanity.com/paper/2304.12000/) (2023)
- [MultiSPANS: A Multi-range Spatial-Temporal Transformer Network for Traffic Forecast via Structural Entropy Optimization](https://mlsanity.com/paper/2311.02880/) (2023)
- [Adversarial Socialbots Modeling Based on Structural Information Principles](https://mlsanity.com/paper/2312.08098/) (2023)
- [Exploring the Potential of Large Language Models for Heterophilic Graphs](https://mlsanity.com/paper/2408.14134/) (2024)
- [Unsupervised Skin Lesion Segmentation via Structural Entropy Minimization on Multi-Scale Superpixel Graphs](https://mlsanity.com/paper/2309.01899/) (2023)
- [HeTGB: A Comprehensive Benchmark for Heterophilic Text-Attributed Graphs](https://mlsanity.com/paper/2503.04822/) (2025)
- [IntraMix: Intra-Class Mixup Generation for Accurate Labels and Neighbors](https://mlsanity.com/paper/2405.00957/) (2024)
- [Effective Exploration Based on the Structural Information Principles](https://mlsanity.com/paper/2410.06621/) (2024)
- [ASIL: Augmented Structural Information Learning for Deep Graph Clustering in Hyperbolic Space](https://mlsanity.com/paper/2504.09970/) (2025)
- [Unsupervised Graph Clustering with Deep Structural Entropy](https://mlsanity.com/paper/2505.14040/) (2025)
- [Bridging Large Language Models and Graph Structure Learning Models for Robust Representation Learning](https://mlsanity.com/paper/2410.12096/) (2024)
- [Rumor Detection on Social Media with Temporal Propagation Structure Optimization](https://mlsanity.com/paper/2412.08316/) (2024)
- [Language Models as Messengers: Enhancing Message Passing in Heterophilic Graph Learning](https://mlsanity.com/paper/2505.19762/) (2025)
- [Principled Data Augmentation for Learning to Solve Quadratic Programming Problems](https://mlsanity.com/paper/2506.01728/) (2025)
- [STAMImputer: Spatio-Temporal Attention MoE for Traffic Data Imputation](https://mlsanity.com/paper/2506.08054/) (2025)
- [Motif-driven Subgraph Structure Learning for Graph Classification](https://mlsanity.com/paper/2406.08897/) (2024)
- [Structural Entropy Guided Probabilistic Coding](https://mlsanity.com/paper/2412.08841/) (2024)
- [GMLM: Bridging Graph Neural Networks and Language Models for Heterophilic Node Classification](https://mlsanity.com/paper/2503.05763/) (2025)
- [Adaptive and Robust DBSCAN with Multi-agent Reinforcement Learning](https://mlsanity.com/paper/2505.04339/) (2025)
- [Towards Effective, Efficient and Unsupervised Social Event Detection in the Hyperbolic Space](https://mlsanity.com/paper/2412.10712/) (2024)
- [Toward Data-centric Directed Graph Learning: An Entropy-driven Approach](https://mlsanity.com/paper/2505.00983/) (2025)
- [When LLM Agents Meet Graph Optimization: An Automated Data Quality Improvement Approach](https://mlsanity.com/paper/2510.08952/) (2025)
- [LANCET: Neural Intervention via Structural Entropy for Mitigating Faithfulness Hallucinations in LLMs](https://mlsanity.com/paper/2601.01401/) (2026)

## Abstract (arXiv)

Graph Neural Networks (GNNs) are de facto solutions to structural data learning. However, it is susceptible to low-quality and unreliable structure, which has been a norm rather than an exception in real-world graphs. Existing graph structure learning (GSL) frameworks still lack robustness and interpretability. This paper proposes a general GSL framework, SE-GSL, through structural entropy and the graph hierarchy abstracted in the encoding tree. Particularly, we exploit the one-dimensional structural entropy to maximize embedded information content when auxiliary neighbourhood attributes are fused to enhance the original graph. A new scheme of constructing optimal encoding trees is proposed to minimize the uncertainty and noises in the graph whilst assuring proper community partition in hierarchical abstraction. We present a novel sample-based mechanism for restoring the graph structure via node structural entropy distribution. It increases the connectivity among nodes with larger uncertainty in lower-level communities. SE-GSL is compatible with various GNN models and enhances the robustness towards noisy and heterophily structures. Extensive experiments show significant improvements in the effectiveness and robustness of structure learning and node representation learning.