Graph machine learning has witnessed rapid growth, driving advancements across diverse domains. However, the in-distribution assumption, where training and testing data share the same distribution, often breaks in real-world scenarios, leading to degraded model performance under distribution shifts. This challenge has catalyzed interest in graph out-of-distribution (GOOD) detection, which focuses on identifying graph data that deviates from the distribution seen during training, thereby enhancing model robustness. In this paper, we provide a rigorous definition of GOOD detection and systematically categorize existing methods into four types: enhancement-based, reconstruction-based, information propagation-based, and classification-based approaches. We analyze the principles and mechanisms of each approach and clarify the distinctions between GOOD detection and related fields, such as graph anomaly detection, outlier detection, and GOOD generalization. Beyond methodology, we discuss practical applications and theoretical foundations, highlighting the unique challenges posed by graph data. Finally, we discuss the primary challenges and propose future directions to advance this emerging field.
⭐The full text is available on arXiv: Out-of-Distribution Detection on Graphs: A Survey
We categorize existing methods into four types: Enhancement-based methods (Enha.), Reconstruction-based methods (Reco.), Information Propagation-based methods (Prop.), and Classification-based methods (Clas.). 👇
Summary of GOOD detection methods (The theoretical and application-oriented papers discussed in Section 8.3 are not included in this table).
| Method | Category | Title | Evaluation Metrics | Datasets | Venue | Paper Links | Code Links | Key Words | Task Type | |
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | GKDE | Clas. | Uncertainty Aware Semi-Supervised Learning on Graph Data | AUROC, AUPR | Cora, Citeseer, Pubmed, Amazon-Photo, Amazon-Computer, Physics-CA | NeurIPS'20 | GKDE | https://github.com/zxj32/uncertainty-GNN | Dirichlet Distribution | Node-Level |
| 2 | OpenWGL | Reco. | OpenWGL: Open-World Graph Learning | ACC., Macor F1 | Cora, Citeseer, DBLP | ICDM'20 | OpenWGL | - | Graph Autoencoder | Node-Level |
| 3 | GPN | Prop. | Graph Posterior Network: Bayesian Predictive Uncertainty for Node Classification | ID-ACC., OOD-ACC., AUROC | CoraML, Amazon-Photos, OGBN-Arxiv | NeurIPS'21 | GPN | https://github.com/stadlmax/Graph-Posterior-Network | Bayesian Posterior | Node-Level |
| 4 | NGC | Prop. | NGC: A Unified Framework for Learning with Open-World Noisy Data | ACC. | CIFAR-10, CIFAR-100, TinyImageNet, Places-365 | ICCV'21 | NGC | - | Contrastive Leaning | Graph-Level |
| 5 | S-BGCN-T-K | Clas. | Uncertainty-Aware Graph-Based Multimodal Remote Sensing Detection of Out-Of-Distribution Samples | AUROC, AUPR | 2018 IEEE GRSS Data Fusion Challenge dataset | CIKM'21 | S-BGCN-T-K | - | Knowledge Distillation | Node-Level |
| 6 | OODGAT | Prop. | Learning on Graphs with Out-of-Distribution Nodes | ACC., AUROC, FPR@95, Macor F1 | Cora, Amazon-CS, Amazon-Photo, Coauthor-CS, LastFMAsia, Wiki-CS | KDD'22 | OODGAT | https://github.com/SongYYYY/KDD22-OODGAT | Semi-Supervised Learning | Node-Level |
| 7 | LMN | Prop. | End-to-End Open-Set Semi-Supervised Node Classification with Out-of-Distribution Detection | ACC. | Cora, Citeseer,Pubmed, arVix | IJCAI'22 | LMN | - | Semi-Supervised Learning | Node-Level |
| 8 | GraphDE | Enha. | GraphDE: A Generative Framework for Debiased Learning and Out-of-Distribution Detection on Graphs | AUROC, AUPR, FPR@95 | Spurious-Motif, MNIST-75sp, Collab, DrugOOD | NeurIPS'22 | GraphDE | https://github.com/Emiyalzn/GraphDE | Generative Model | Graph-Level |
| 9 | OSSC | Reco. | A Dynamic Variational Framework for Open-World Node Classification in Structured Sequences | ACC., AUC, Macor F1 | DBLP-5, DBLP-3, Reddit, Brain | ICDM'22 | OSSC | https://github.com/qinzhang11/OSSC | Graph Autoencoder | Node-Level |
| 10 | EL | Clas. | Well-Classified Examples are Underestimated in Classification with Deep Neural Networks | ACC. | Proteins, NCI1 | AAAI'22 | EL | https://github.com/lancopku/well-classified-examples-are-underestimated | Self-Supervised Learning | Node- & Graph-Level |
| 11 | AAGOD | Clas. | A Data-centric Framework to Endow Graph Neural Networks with Out-Of-Distribution Detection Ability | AUC, AUPR, FPR@95 | ENZYMES, PROTEIN, IMDBM, IMDBB, BZR, COX2, TOX21, SIDER, BBBP, BACE | KDD'23 | AAGOD | https://github.com/BUPT-GAMMA/AAGOD | Self-Supervised Learning | Graph-Level |
| 12 | GNNSafe | Prop. | Energy-Based Out-of-Distribution Detection for Graph Neural Networks | ACC., AUROC, AUPR, FPR@95 | Twitch, Arxiv, Cora, Amazon-Photo, Coauthor-CS | ICLR'23 | GNNSafe | https://github.com/qitianwu/GraphOOD-GNNSafe | Energy-Based Model | Node-Level |
| 13 | GOOD-D | Enha. | GOOD-D: On Unsupervised Graph Out-Of-Distribution Detection | AUC | BZR, PTC-MR, AIDS, ENZYMES, IMDB-M, Tox21, FreeSolv, BBBP, ClinTox, Esol, COX2, MUTAG, DHFR, PROTEIN, IMDB-B, SIDER, ToxCast, BACE, LIPO, MUV | WSDM'23 | GOOD-D | https://github.com/yixinliu233/G-OOD-D | Contrastive Leaning | Graph-Level |
| 14 | Relation | Clas. | Neural Relation Graph: A Unified Framework for Identifying Label Noise and Outlier Data | AP, TNR95 | ImageNet, Places, SUN, iNatualist, Textures | NeurIPS'23 | Relation | https://github.com/snu-mllab/Neural-Relation-Graph | Semi-Supervised Learning | Graph-Level |
| 15 | GPN-CE-GD | Enha. | Improvements on Uncertainty Quantification for Node Classification via Distance-Based Regularization | ID-ACC., AUROC, AUPR | CoraML, Citeseer, PubMed | NeurIPS'23 | GPN-CE-GD | https://github.com/neoques/Graph-Posterior-Network | Bayesian Posterior | Node-Level |
| 16 | Open-WRF | Prop. | Open-World Lifelong Graph Learning | ACC., AUROC | Cora, Citeseer, Pubmed, OGB-arXiv, DBLP-easy, DBLP-hard | IJCNN'23 | Open-WRF | https://github.com/Bobowner/Open-World-LGL | Weakly-Supervised Learning | Node- & Graph-Level |
| 17 | UGNN | Clas. | Towards Semi-Supervised Universal Graph Classification | ACC. | COIL-DEL, Letter-High, MNIST, CIFAR10, Reddit-Mutil-12k, Colors-3 | TKDE'23 | UGNN | - | Semi-Supervised Learning | Graph-Level |
| 18 | GERDQ | Prop. | Calibrate Graph Neural Networks under Out-of-Distribution Nodes via Deep Q-learning | ACC., ECE | Cora, Citeseer, Pubmed, Amazon-Photo, Amazon-Computer, Physics-CA | CIKM'23 | GERDQ | https://github.com/DamoSWL/Calibration-of-GNN-with-OOD-nodes | Deep Q-Learning | Node-Level |
| 19 | SGOOD | Enha. | SGOOD: Substructure-enhanced Graph-Level Out-of-Distribution Detection | AUROC, AUPR, FPR@95 | ENZYMES, IMDB-M, IMDB-B, Reddit-12k, BACE, BBBP, DrugOOD, HIV | CIKM'24 | SGOOD | https://github.com/TommyDzh/SGOOD | Self-Supervised Learning | Graph-Level |
| 20 | GOODAT | Enha. | GOODAT: Towards Test-time Graph Out-of-Distribution Detection | AUC | BZR, PTC-MR, AIDS, ENZYMES, IMDB-M, Tox21, FreeSolv, BBBP, ClinTox, Esol, COX2, MUTAG, DHFR, PROTEIN, IMDB-B, SIDER, ToxCast, BACE, LIPO, MUV | AAAI'24 | GOODAT | - | Information Bottleneck | Graph-Level |
| 21 | TopoOOD | Prop. | Graph Out-of-Distribution Detection Goes Neighborhood Shaping | ACC., AUROC, AUPR, FPR@95 | Twitch, Arxiv, Cora, Amazon, Coauthor | ICML'24 | TopoOOD | - | Dirichlet Energy | Node-Level |
| 22 | NODESAFE | Prop. | Bounded and Uniform Energy-based Out-of-distribution Detection for Graphs | ACC., AUROC, AUPR, FPR@95 | Twitch, Arxiv, Cora, Amazon, Coauthor | ICML'24 | NODESAFE | https://github.com/ShenzhiYang2000/NODESAFE | Energy-Based Model | Node-Level |
| 23 | GNSD | Prop. | Graph Neural Stochastic Diffusion for Estimating Uncertainty in Node Classification | ACC., AUROC, AUPR, FPR@95 | Amazon-Computers, Cora, Citeseer, Pubmed, Arxiv | ICML'24 | GNSD | - | Diffusion Model | Node-Level |
| 24 | PGR-MOOD | Reco. | Optimizing OOD Detection in Molecular Graphs: A Novel Approach with Diffusion Models | AUROC, AUPR, FPR@95 | GOOD-HIV, GOOD-PCBA, DrugOOD-IC50, DrugOOD-EC50 | KDD'24 | PGR-MOOD | https://github.com/se7esx/PGR-MOOD | Diffusion Model | Graph-Level |
| 25 | EnergyDef | Prop. | An Energy-centric Framework for Category-free Out-of-distribution Node Detection in Graphs | AUROC, AUPR, FPR@95 | Squirrel, WikiCS, YelpChi, Amazon, Reddit | KDD'24 | EnergyDef | https://github.com/KellyGong/EnergyDef | Energy-Based Model | Node-Level |
| 26 | HGOE | Enha. | HGOE: Hybrid External and Internal Graph Outlier Exposure for Graph Out-of-Distribution Detection | AUC | AIDS, DHFR, ENZYMES, PROTEIN, IMDB-M, IMDB-B, Tox21, SIDER, FreeSolv, ToxCast, BBBP, BACE, ClinTox, LIPO, Esol, MUV, BZR, COX2, PTC_MR, MUTAG | MM'24 | HGOE | - | Outlier Exposure | Graph-Level |
| 27 | SMUG | Enha. | SMUG: Sand Mixing for Unobserved Class Detection in Graph Few-Shot Learning | AUROC | Cora, DBLP, Amazon-Clothing, Amazon-Electronics | WWW'24 | SMUG | - | Few-Shot Learning | Node-Level |
| 28 | ML-GOOD | Prop. | ML-GOOD: Towards Multi-Label Graph Out-Of-Distribution Detection | ACC., AUROC, AUPR, FPR@95 | OGB-Proteins, PPI, DBLP, PCG, HumLoc, EukLoc | AAAI'25 | ML-GOOD | https://github.com/ca1man-2022/ML-GOOD | Energy-Based Model | Node-Level |
| 29 | GRASP | Prop. | Revisiting Score Propagation in Graph Out-of-Distribution Detection | AUROC, FPR@95 | Arxiv-year, Cora, Amazon, Coauthor, Chameleon, Squirrel, Reddit2, ogbn-Product, snap-patents, wiki | NeurIPS'24 | GRASP | https://github.com/longfei-ma/GRASP | Graph Augmentation | Node-Level |
| 30 | GOLD | Enha. | GOLD: Graph Out-of-Distribution Detection via Implicit Adversarial Latent Generation | AUROC, FPR@95 | Twitch, Arxiv, Cora, Amazon, Coauthor | ICLR'25 | GOLD | https://github.com/DannyW618/GOLD | Generative Model | Node-Level |
| 31 | DeGEM | Enha. | Decoupled Graph Energy-based Model for Node Out-of-Distribution Detection on Heterophilic Graphs | AUROC, FPR@95 | Twitch, Arxiv, ogbn-Cora, Amazon-Photo, Chameleon, Actor, Cornell | ICLR'25 | DeGEM | - | Energy-Based Model | Node-Level |
| 32 | EDBD | Prop. | Spreading Out-of-Distribution Detection on Graphs | AUROC, FPR@95 | Cora, Amazon-Photo, Amazon-Computers, Coauthor-CS | ICLR'25 | EDBD | - | Energy-Based Model | Node-Level |