# Structural Entropy Guided Unsupervised Graph Out-Of-Distribution Detection

arXiv: https://arxiv.org/abs/2503.03241 · HTML: https://mlsanity.com/paper/2503.03241/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 50 references that are in the map.
- First posted on arXiv 5 Mar 2025.

## Builds on (most cited first, 28 of 28)

- [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)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [Self-supervised Learning: Generative or Contrastive](https://mlsanity.com/paper/2006.08218/) (2020)
- [Contrastive Multi-View Representation Learning on Graphs](https://mlsanity.com/paper/2006.05582/) (2020)
- [On Variational Bounds of Mutual Information](https://mlsanity.com/paper/1905.06922/) (2019)
- [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)
- [On Mutual Information Maximization for Representation Learning](https://mlsanity.com/paper/1907.13625/) (2019)
- [Graph Self-Supervised Learning: A Survey](https://mlsanity.com/paper/2103.00111/) (2021)
- [SSD: A Unified Framework for Self-Supervised Outlier Detection](https://mlsanity.com/paper/2103.12051/) (2021)
- [Graph Information Bottleneck](https://mlsanity.com/paper/2010.12811/) (2020)
- [Propagation Kernels](https://mlsanity.com/paper/1410.3314/) (2014)
- [Contrastive Out-of-Distribution Detection for Pretrained Transformers](https://mlsanity.com/paper/2104.08812/) (2021)
- [Rethinking and Scaling Up Graph Contrastive Learning: An Extremely Efficient Approach with Group Discrimination](https://mlsanity.com/paper/2206.01535/) (2022)
- [Deep Graph-level Anomaly Detection by Glocal Knowledge Distillation](https://mlsanity.com/paper/2112.10063/) (2021)
- [Structural Entropy Guided Graph Hierarchical Pooling](https://mlsanity.com/paper/2206.13510/) (2022)
- [NGC: A Unified Framework for Learning with Open-World Noisy Data](https://mlsanity.com/paper/2108.11035/) (2021)
- [On Using Classification Datasets to Evaluate Graph-Level Outlier Detection: Peculiar Observations and New Insights](https://mlsanity.com/paper/2012.12931/) (2020)
- [A Simple yet Effective Method for Graph Classification](https://mlsanity.com/paper/2206.02404/) (2022)
- [Unifying Graph Contrastive Learning with Flexible Contextual Scopes](https://mlsanity.com/paper/2210.08792/) (2022)
- [NC-NCD: Novel Class Discovery for Node Classification](https://mlsanity.com/paper/2407.17816/) (2024)

## Built on by (most cited first, 3 of 3)

- [Toward Robust Signed Graph Learning through Joint Input-Target Denoising](https://mlsanity.com/paper/2510.22513/) (2025)
- [Improving LLM Reasoning with Homophily-aware Structural and Semantic Text-Attributed Graph Compression](https://mlsanity.com/paper/2601.08187/) (2026)
- [Disentangled Graph Prompting for Out-Of-Distribution Detection](https://mlsanity.com/paper/2603.29644/) (2026)

## Abstract (arXiv)

With the emerging of huge amount of unlabeled data, unsupervised out-of-distribution (OOD) detection is vital for ensuring the reliability of graph neural networks (GNNs) by identifying OOD samples from in-distribution (ID) ones during testing, where encountering novel or unknown data is inevitable. Existing methods often suffer from compromised performance due to redundant information in graph structures, which impairs their ability to effectively differentiate between ID and OOD data. To address this challenge, we propose SEGO, an unsupervised framework that integrates structural entropy into OOD detection regarding graph classification. Specifically, within the architecture of contrastive learning, SEGO introduces an anchor view in the form of coding tree by minimizing structural entropy. The obtained coding tree effectively removes redundant information from graphs while preserving essential structural information, enabling the capture of distinct graph patterns between ID and OOD samples. Furthermore, we present a multi-grained contrastive learning scheme at local, global, and tree levels using triplet views, where coding trees with essential information serve as the anchor view. Extensive experiments on real-world datasets validate the effectiveness of SEGO, demonstrating superior performance over state-of-the-art baselines in OOD detection. Specifically, our method achieves the best performance on 9 out of 10 dataset pairs, with an average improvement of 3.7% on OOD detection datasets, significantly surpassing the best competitor by 10.8% on the FreeSolv/ToxCast dataset pair.