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A Survey on Graph Counterfactual Explanations: Definitions, Methods, Evaluation, and Research Challenges

Mario Alfonso Prado-Romero, Bardh Prenkaj, Giovanni Stilo, Fosca Giannotti

TL;DR

This survey tackles graph counterfactual explanations (GCE) for Graph Neural Networks by introducing a uniform formalism and a comprehensive taxonomy, enabling consistent comparisons across methods. It consolidates definitions for minimal and multi-class counterfactuals, and documents standardized evaluation protocols and datasets, supplemented by an empirical study via the GRETEL framework. Key contributions include a formal multi-class GCE definition, a ten-dimensional method taxonomy, and a reproducible evaluation platform that highlights strengths and pitfalls across domains such as social, molecular, and -omics graphs. The work also discusses privacy and fairness considerations and maps out open challenges, guiding future research toward model-level explanations, edge-prediction tasks, and robust benchmarks with open competitions. The findings underscore that no single method dominates across all settings; effectiveness is highly domain- and task-dependent, underscoring the need for diverse, reproducible evaluation practices in graph counterfactual explainability.

Abstract

Graph Neural Networks (GNNs) perform well in community detection and molecule classification. Counterfactual Explanations (CE) provide counter-examples to overcome the transparency limitations of black-box models. Due to the growing attention in graph learning, we focus on the concepts of CE for GNNs. We analysed the SoA to provide a taxonomy, a uniform notation, and the benchmarking datasets and evaluation metrics. We discuss fourteen methods, their evaluation protocols, twenty-two datasets, and nineteen metrics. We integrated the majority of methods into the GRETEL library to conduct an empirical evaluation to understand their strengths and pitfalls. We highlight open challenges and future work.

A Survey on Graph Counterfactual Explanations: Definitions, Methods, Evaluation, and Research Challenges

TL;DR

This survey tackles graph counterfactual explanations (GCE) for Graph Neural Networks by introducing a uniform formalism and a comprehensive taxonomy, enabling consistent comparisons across methods. It consolidates definitions for minimal and multi-class counterfactuals, and documents standardized evaluation protocols and datasets, supplemented by an empirical study via the GRETEL framework. Key contributions include a formal multi-class GCE definition, a ten-dimensional method taxonomy, and a reproducible evaluation platform that highlights strengths and pitfalls across domains such as social, molecular, and -omics graphs. The work also discusses privacy and fairness considerations and maps out open challenges, guiding future research toward model-level explanations, edge-prediction tasks, and robust benchmarks with open competitions. The findings underscore that no single method dominates across all settings; effectiveness is highly domain- and task-dependent, underscoring the need for diverse, reproducible evaluation practices in graph counterfactual explainability.

Abstract

Graph Neural Networks (GNNs) perform well in community detection and molecule classification. Counterfactual Explanations (CE) provide counter-examples to overcome the transparency limitations of black-box models. Due to the growing attention in graph learning, we focus on the concepts of CE for GNNs. We analysed the SoA to provide a taxonomy, a uniform notation, and the benchmarking datasets and evaluation metrics. We discuss fourteen methods, their evaluation protocols, twenty-two datasets, and nineteen metrics. We integrated the majority of methods into the GRETEL library to conduct an empirical evaluation to understand their strengths and pitfalls. We highlight open challenges and future work.
Paper Structure (34 sections, 23 equations, 10 figures, 9 tables)

This paper contains 34 sections, 23 equations, 10 figures, 9 tables.

Table of Contents

  1. Introduction
  2. Contributions of this survey
  3. Defining counterfactual explanations in graphs
  4. Unifying GCE definitions in the literature
  5. Minimal graph counterfactual explanations
  6. Methods
  7. Graph Counterfactual Explainability Taxonomy
  8. GCE literature classification
  9. GCE Methods
  10. Evaluation
  11. Datasets adopted in the literature
  12. Evaluation Metrics
  13. Adopted evaluation protocols for GCE
  14. Empirical evaluation of GCE methods
  15. Privacy of Explainers and Fairness of Oracles in GCE
  16. ...and 19 more sections

Figures (10)

  • Figure 1: Drug repurposing mechanism. Passing from cephalexin (left) to amoxicillin (right) by removing atoms and reforming hexagonal connections into pentagons. Here, the counterfactual explanation consists of the highlighted edges and vertices.
  • Figure 2: Taxonomy of Graph Counterfactual Explanation (GCE) methods.
  • Figure 3: An example of a 5-Nitroacenaphthene molecular structure. (left) Factual example, represented as bold connections, as a Nitrobenzene molecule. (middle) Derived counterfactual example by eliminating the Nitrobenzene molecule. (right) Minimal counterfactual example highlighting the three connections that, if removed, break the Nitrobenzene structure avoiding the molecule being a carcinogen.
  • Figure 4: Workflow of privacy-preserving counterfactual explainers.
  • Figure 5: End-to-end prediction task of a GNN model.
  • ...and 5 more figures

Theorems & Definitions (4)

  • definition 1
  • definition 2
  • definition 3
  • definition 4