# Understanding Isomorphism Bias in Graph Data Sets

arXiv: https://arxiv.org/abs/1910.12091 · HTML: https://mlsanity.com/paper/1910.12091/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Oct 2019.

## Built on by (most cited first, 23 of 23)

- [1-WL Expressiveness Is (Almost) All You Need](https://mlsanity.com/paper/2202.10156/) (2022)
- [TopoImb: Toward Topology-level Imbalance in Learning from Graphs](https://mlsanity.com/paper/2212.08689/) (2022)
- [GNNX-BENCH: Unravelling the Utility of Perturbation-based GNN Explainers through In-depth Benchmarking](https://mlsanity.com/paper/2310.01794/) (2023)
- [Graph Edit Distance with General Costs Using Neural Set Divergence](https://mlsanity.com/paper/2409.17687/) (2024)
- [Weisfeiler and Leman Go Walking: Random Walk Kernels Revisited](https://mlsanity.com/paper/2205.10914/) (2022)
- [AutoTransfer: AutoML with Knowledge Transfer -- An Application to Graph Neural Networks](https://mlsanity.com/paper/2303.07669/) (2023)
- [Total Variation Graph Neural Networks](https://mlsanity.com/paper/2211.06218/) (2022)
- [State of the Art and Potentialities of Graph-level Learning](https://mlsanity.com/paper/2301.05860/) (2023)
- [Graph as Point Set](https://mlsanity.com/paper/2405.02795/) (2024)
- [PreGIP: Watermarking the Pretraining of Graph Neural Networks for Deep Intellectual Property Protection](https://mlsanity.com/paper/2402.04435/) (2024)
- [Graph Counterfactual Explainable AI via Latent Space Traversal](https://mlsanity.com/paper/2501.08850/) (2025)
- [Position: Don't be Afraid of Over-Smoothing And Over-Squashing](https://mlsanity.com/paper/2601.07419/) (2026)
- [KAA: Kolmogorov-Arnold Attention for Enhancing Attentive Graph Neural Networks](https://mlsanity.com/paper/2501.13456/) (2025)
- [Graph-level Neural Networks: Current Progress and Future Directions](https://mlsanity.com/paper/2205.15555/) (2022)
- [Tired of Over-smoothing? Stress Graph Drawing Is All You Need!](https://mlsanity.com/paper/2211.10579/) (2022)
- [ID-MixGCL: Identity Mixup for Graph Contrastive Learning](https://mlsanity.com/paper/2304.10045/) (2023)
- [Weisfeiler and Leman Go Measurement Modeling: Probing the Validity of the WL Test](https://mlsanity.com/paper/2307.05775/) (2023)
- [EUGENE: Explainable Structure-aware Graph Edit Distance Estimation with Generalized Edit Costs](https://mlsanity.com/paper/2402.05885/) (2024)
- [A Structural Feature-Based Approach for Comprehensive Graph Classification](https://mlsanity.com/paper/2408.05474/) (2024)
- [Predicting Steady-State Behavior in Complex Networks with Graph Neural Networks](https://mlsanity.com/paper/2502.01693/) (2025)
- [CryptGNN: Enabling Secure Inference for Graph Neural Networks](https://mlsanity.com/paper/2509.09107/) (2025)
- [BadImplant: Injection-based Multi-Targeted Graph Backdoor Attack](https://mlsanity.com/paper/2601.15474/) (2026)
- [PATTERN Can Be Solved from Memory: Generator-Aware Baselines for Synthetic Node Classification](https://mlsanity.com/paper/2610.15020/) (2026)

## Abstract (arXiv)

In recent years there has been a rapid increase in classification methods on graph structured data. Both in graph kernels and graph neural networks, one of the implicit assumptions of successful state-of-the-art models was that incorporating graph isomorphism features into the architecture leads to better empirical performance. However, as we discover in this work, commonly used data sets for graph classification have repeating instances which cause the problem of isomorphism bias, i.e. artificially increasing the accuracy of the models by memorizing target information from the training set. This prevents fair competition of the algorithms and raises a question of the validity of the obtained results. We analyze 54 data sets, previously extensively used for graph-related tasks, on the existence of isomorphism bias, give a set of recommendations to machine learning practitioners to properly set up their models, and open source new data sets for the future experiments.