# KerGNNs: Interpretable Graph Neural Networks with Graph Kernels

arXiv: https://arxiv.org/abs/2201.00491 · HTML: https://mlsanity.com/paper/2201.00491/

## Key facts

- Cited by 50 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 53 references that are in the map.
- First posted on arXiv 3 Jan 2022.

## Builds on (most cited first, 30 of 32)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [GNNExplainer: Generating Explanations for Graph Neural Networks](https://mlsanity.com/paper/1903.03894/) (2019)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [Provably Powerful Graph Networks](https://mlsanity.com/paper/1905.11136/) (2019)
- [Dynamic Edge-Conditioned Filters in Convolutional Neural Networks on Graphs](https://mlsanity.com/paper/1704.02901/) (2017)
- [A Fair Comparison of Graph Neural Networks for Graph Classification](https://mlsanity.com/paper/1912.09893/) (2019)
- [Graph Neural Tangent Kernel: Fusing Graph Neural Networks with Graph Kernels](https://mlsanity.com/paper/1905.13192/) (2019)
- [Explainability Techniques for Graph Convolutional Networks](https://mlsanity.com/paper/1905.13686/) (2019)
- [A Survey on Graph Kernels](https://mlsanity.com/paper/1903.11835/) (2019)
- [Propagation Kernels](https://mlsanity.com/paper/1410.3314/) (2014)
- [Approximation Ratios of Graph Neural Networks for Combinatorial Problems](https://mlsanity.com/paper/1905.10261/) (2019)
- [GraKeL: A Graph Kernel Library in Python](https://mlsanity.com/paper/1806.02193/) (2018)
- [Convolutional Kernel Networks](https://mlsanity.com/paper/1406.3332/) (2014)
- [Convolutional Kernel Networks for Graph-Structured Data](https://mlsanity.com/paper/2003.05189/) (2020)
- [End-to-End Kernel Learning with Supervised Convolutional Kernel Networks](https://mlsanity.com/paper/1605.06265/) (2016)
- [Graph Homomorphism Convolution](https://mlsanity.com/paper/2005.01214/) (2020)
- [Deriving Neural Architectures from Sequence and Graph Kernels](https://mlsanity.com/paper/1705.09037/) (2017)

## Built on by (most cited first, 30 of 50)

- [Trustworthy Graph Neural Networks: Aspects, Methods and Trends](https://mlsanity.com/paper/2205.07424/) (2022)
- [CoCo: A Coupled Contrastive Framework for Unsupervised Domain Adaptive Graph Classification](https://mlsanity.com/paper/2306.04979/) (2023)
- [A Survey on Explainability of Graph Neural Networks](https://mlsanity.com/paper/2306.01958/) (2023)
- [A Comprehensive Survey on Self-Interpretable Neural Networks](https://mlsanity.com/paper/2501.15638/) (2025)
- [Graph Neural Networks in Particle Physics: Implementations, Innovations, and Challenges](https://mlsanity.com/paper/2203.12852/) (2022)
- [A Survey on Malware Detection with Graph Representation Learning](https://mlsanity.com/paper/2303.16004/) (2023)
- [Explaining Graph Neural Networks via Structure-aware Interaction Index](https://mlsanity.com/paper/2405.14352/) (2024)
- [Motif-based Graph Representation Learning with Application to Chemical Molecules](https://mlsanity.com/paper/2208.04529/) (2022)
- [Kernel-based Substructure Exploration for Next POI Recommendation](https://mlsanity.com/paper/2210.03969/) (2022)
- [Unveiling Global Interactive Patterns across Graphs: Towards Interpretable Graph Neural Networks](https://mlsanity.com/paper/2407.01979/) (2024)
- [Urban Region Pre-training and Prompting: A Graph-based Approach](https://mlsanity.com/paper/2408.05920/) (2024)
- [L2XGNN: Learning to Explain Graph Neural Networks](https://mlsanity.com/paper/2209.14402/) (2022)
- [Recent Advances in Malware Detection: Graph Learning and Explainability](https://mlsanity.com/paper/2502.10556/) (2025)
- [Interpretable Graph Neural Networks for Tabular Data](https://mlsanity.com/paper/2308.08945/) (2023)
- [How Faithful are Self-Explainable GNNs?](https://mlsanity.com/paper/2308.15096/) (2023)
- [Descriptive Kernel Convolution Network with Improved Random Walk Kernel](https://mlsanity.com/paper/2402.06087/) (2024)
- [Incorporating Heterophily into Graph Neural Networks for Graph Classification](https://mlsanity.com/paper/2203.07678/) (2022)
- [From GNNs to Trees: Multi-Granular Interpretability for Graph Neural Networks](https://mlsanity.com/paper/2505.00364/) (2025)
- [B-XAIC Dataset: Benchmarking Explainable AI for Graph Neural Networks Using Chemical Data](https://mlsanity.com/paper/2505.22252/) (2025)
- [Unsupervised Neighborhood Propagation Kernel Layers for Semi-supervised Node Classification](https://mlsanity.com/paper/2301.13764/) (2023)
- [Structure-Aware DropEdge Towards Deep Graph Convolutional Networks](https://mlsanity.com/paper/2306.12091/) (2023)
- [Prediction via Shapley Value Regression](https://mlsanity.com/paper/2505.04775/) (2025)
- [MoSE: Unveiling Structural Patterns in Graphs via Mixture of Subgraph Experts](https://mlsanity.com/paper/2509.09337/) (2025)
- [The End of Reward Engineering: How LLMs Are Redefining Multi-Agent Coordination](https://mlsanity.com/paper/2601.08237/) (2026)
- [Augment to Interpret: Unsupervised and Inherently Interpretable Graph Embeddings](https://mlsanity.com/paper/2309.16564/) (2023)
- [Self-supervision meets kernel graph neural models: From architecture to augmentations](https://mlsanity.com/paper/2310.11281/) (2023)
- [Learning Attributed Graphlets: Predictive Graph Mining by Graphlets with Trainable Attribute](https://mlsanity.com/paper/2402.06932/) (2024)
- [Discovering robust biomarkers of psychiatric disorders from resting-state functional MRI via graph neural networks: A systematic review](https://mlsanity.com/paper/2405.00577/) (2024)
- [ENADPool: The Edge-Node Attention-based Differentiable Pooling for Graph Neural Networks](https://mlsanity.com/paper/2405.10218/) (2024)
- [Topology Reorganized Graph Contrastive Learning with Mitigating Semantic Drift](https://mlsanity.com/paper/2407.16726/) (2024)

## Abstract (arXiv)

Graph kernels are historically the most widely-used technique for graph classification tasks. However, these methods suffer from limited performance because of the hand-crafted combinatorial features of graphs. In recent years, graph neural networks (GNNs) have become the state-of-the-art method in downstream graph-related tasks due to their superior performance. Most GNNs are based on Message Passing Neural Network (MPNN) frameworks. However, recent studies show that MPNNs can not exceed the power of the Weisfeiler-Lehman (WL) algorithm in graph isomorphism test. To address the limitations of existing graph kernel and GNN methods, in this paper, we propose a novel GNN framework, termed textitKernel Graph Neural Networks (KerGNNs), which integrates graph kernels into the message passing process of GNNs. Inspired by convolution filters in convolutional neural networks (CNNs), KerGNNs adopt trainable hidden graphs as graph filters which are combined with subgraphs to update node embeddings using graph kernels. In addition, we show that MPNNs can be viewed as special cases of KerGNNs. We apply KerGNNs to multiple graph-related tasks and use cross-validation to make fair comparisons with benchmarks. We show that our method achieves competitive performance compared with existing state-of-the-art methods, demonstrating the potential to increase the representation ability of GNNs. We also show that the trained graph filters in KerGNNs can reveal the local graph structures of the dataset, which significantly improves the model interpretability compared with conventional GNN models.