# Graph Kernel Neural Networks

arXiv: https://arxiv.org/abs/2112.07436 · HTML: https://mlsanity.com/paper/2112.07436/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 83 references that are in the map.
- First posted on arXiv 14 Dec 2021.

## Builds on (most cited first, 30 of 36)

- [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)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- [Improving Graph Neural Network Expressivity via Subgraph Isomorphism Counting](https://mlsanity.com/paper/2006.09252/) (2020)
- [Dynamic Edge-Conditioned Filters in Convolutional Neural Networks on Graphs](https://mlsanity.com/paper/1704.02901/) (2017)
- [Diffusion-Convolutional Neural Networks](https://mlsanity.com/paper/1511.02136/) (2015)
- [A Fair Comparison of Graph Neural Networks for Graph Classification](https://mlsanity.com/paper/1912.09893/) (2019)
- [CayleyNets: Graph Convolutional Neural Networks with Complex Rational Spectral Filters](https://mlsanity.com/paper/1705.07664/) (2017)
- [Graph Neural Tangent Kernel: Fusing Graph Neural Networks with Graph Kernels](https://mlsanity.com/paper/1905.13192/) (2019)
- [Equivariant Subgraph Aggregation Networks](https://mlsanity.com/paper/2110.02910/) (2021)
- [A Survey on Graph Kernels](https://mlsanity.com/paper/1903.11835/) (2019)
- [A Survey on The Expressive Power of Graph Neural Networks](https://mlsanity.com/paper/2003.04078/) (2020)
- [PDE-GCN: Novel Architectures for Graph Neural Networks Motivated by Partial Differential Equations](https://mlsanity.com/paper/2108.01938/) (2021)
- [Generalized Jensen-Shannon Divergence Loss for Learning with Noisy Labels](https://mlsanity.com/paper/2105.04522/) (2021)
- [On Provable Benefits of Depth in Training Graph Convolutional Networks](https://mlsanity.com/paper/2110.15174/) (2021)
- [k-hop Graph Neural Networks](https://mlsanity.com/paper/1907.06051/) (2019)
- [Convolutional Kernel Networks for Graph-Structured Data](https://mlsanity.com/paper/2003.05189/) (2020)
- [Deriving Neural Architectures from Sequence and Graph Kernels](https://mlsanity.com/paper/1705.09037/) (2017)
- [Learning Backtrackless Aligned-Spatial Graph Convolutional Networks for Graph Classification](https://mlsanity.com/paper/1904.04238/) (2019)
- [Partition and Code: learning how to compress graphs](https://mlsanity.com/paper/2107.01952/) (2021)
- [A Quantum-inspired Similarity Measure for the Analysis of Complete Weighted Graphs](https://mlsanity.com/paper/1904.13239/) (2019)

## Built on by (most cited first, 13 of 13)

- [CoCo: A Coupled Contrastive Framework for Unsupervised Domain Adaptive Graph Classification](https://mlsanity.com/paper/2306.04979/) (2023)
- [Motif-based Graph Representation Learning with Application to Chemical Molecules](https://mlsanity.com/paper/2208.04529/) (2022)
- [GALA: Graph Diffusion-based Alignment with Jigsaw for Source-free Domain Adaptation](https://mlsanity.com/paper/2410.16606/) (2024)
- [Descriptive Kernel Convolution Network with Improved Random Walk Kernel](https://mlsanity.com/paper/2402.06087/) (2024)
- [Graph-in-Graph (GiG): Learning interpretable latent graphs in non-Euclidean domain for biological and healthcare applications](https://mlsanity.com/paper/2204.00323/) (2022)
- [B-XAIC Dataset: Benchmarking Explainable AI for Graph Neural Networks Using Chemical Data](https://mlsanity.com/paper/2505.22252/) (2025)
- [A Comparison of Graph Neural Networks for Malware Classification](https://mlsanity.com/paper/2303.12812/) (2023)
- [Explaining the Power of Topological Data Analysis in Graph Machine Learning](https://mlsanity.com/paper/2401.04250/) (2024)
- [VGFL-SA: Vertical Graph Federated Learning Structure Attack Based on Contrastive Learning](https://mlsanity.com/paper/2502.16793/) (2025)
- [GNN-LoFI: a Novel Graph Neural Network through Localized Feature-based Histogram Intersection](https://mlsanity.com/paper/2401.09193/) (2024)
- [Flexible Infinite-Width Graph Convolutional Neural Networks](https://mlsanity.com/paper/2402.06525/) (2024)
- [LGRPool: Hierarchical Graph Pooling Via Local-Global Regularisation](https://mlsanity.com/paper/2504.08530/) (2025)
- [Are Graph Attention Networks Able to Model Structural Information?](https://mlsanity.com/paper/2505.21288/) (2025)

## Abstract (arXiv)

The convolution operator at the core of many modern neural architectures can effectively be seen as performing a dot product between an input matrix and a filter. While this is readily applicable to data such as images, which can be represented as regular grids in the Euclidean space, extending the convolution operator to work on graphs proves more challenging, due to their irregular structure. In this paper, we propose to use graph kernels, i.e. kernel functions that compute an inner product on graphs, to extend the standard convolution operator to the graph domain. This allows us to define an entirely structural model that does not require computing the embedding of the input graph. Our architecture allows to plug-in any type of graph kernels and has the added benefit of providing some interpretability in terms of the structural masks that are learned during the training process, similarly to what happens for convolutional masks in traditional convolutional neural networks. We perform an extensive ablation study to investigate the model hyper-parameters' impact and show that our model achieves competitive performance on standard graph classification and regression datasets.