# A Comparative Study of Counterfactual Explainers for Graph Neural Networks Enabling Multiple Types of Graph Edit

arXiv: https://arxiv.org/abs/2609.05113 · HTML: https://mlsanity.com/paper/2609.05113/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 34 references that are in the map.
- First posted on arXiv 4 Sep 2026.

## Builds on (most cited first, 17 of 17)

- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Parameterized Explainer for Graph Neural Network](https://mlsanity.com/paper/2011.04573/) (2020)
- [On Explainability of Graph Neural Networks via Subgraph Explorations](https://mlsanity.com/paper/2102.05152/) (2021)
- [XGNN: Towards Model-Level Explanations of Graph Neural Networks](https://mlsanity.com/paper/2006.02587/) (2020)
- [Interpreting Graph Neural Networks for NLP With Differentiable Edge Masking](https://mlsanity.com/paper/2010.00577/) (2020)
- [A Comprehensive Survey on Trustworthy Graph Neural Networks: Privacy, Robustness, Fairness, and Explainability](https://mlsanity.com/paper/2204.08570/) (2022)
- [Learning and Evaluating Graph Neural Network Explanations based on Counterfactual and Factual Reasoning](https://mlsanity.com/paper/2202.08816/) (2022)
- [Towards Self-Explainable Graph Neural Network](https://mlsanity.com/paper/2108.12055/) (2021)
- [Robust Counterfactual Explanations on Graph Neural Networks](https://mlsanity.com/paper/2107.04086/) (2021)
- [CLEAR: Generative Counterfactual Explanations on Graphs](https://mlsanity.com/paper/2210.08443/) (2022)
- [MEG: Generating Molecular Counterfactual Explanations for Deep Graph Networks](https://mlsanity.com/paper/2104.08060/) (2021)
- [Counterfactual Learning on Graphs: A Survey](https://mlsanity.com/paper/2304.01391/) (2023)
- [Graph Neural Networks for Vulnerability Detection: A Counterfactual Explanation](https://mlsanity.com/paper/2404.15687/) (2024)
- [Multi-objective Explanations of GNN Predictions](https://mlsanity.com/paper/2111.14651/) (2021)
- [D4Explainer: In-Distribution GNN Explanations via Discrete Denoising Diffusion](https://mlsanity.com/paper/2310.19321/) (2023)
- [Robust Stochastic Graph Generator for Counterfactual Explanations](https://mlsanity.com/paper/2312.11747/) (2023)
- [Graph Inverse Style Transfer for Counterfactual Explainability](https://mlsanity.com/paper/2505.17542/) (2025)

## Abstract (arXiv)

Counterfactual explanations for graph-structured data seek to determine minimal and realistic modifications required in an input graph to alter a model's prediction to a predefined output. Although counterfactual explainers that support modifying the graph by both adding and removing edges have recently emerged, there is still a lack of general and efficient methods, especially when considering the quality of the generated explanations. Moreover, the problem remains far from solved, as existing methods exhibit different strengths and weaknesses, often trading off between explanation size, coverage and quality. For this reason, it is important to identify where each method performs well and where it falls short, so as to guide future research in the field. Thus, our study compares six state-of-the-art (SOTA) models on a diverse set of real-world and synthetic datasets, covering both binary and multi-class graph and node classification tasks, and evaluates their performance using diverse quantitative and qualitative metrics.