# Bridging the Gap Between Spectral and Spatial Domains in Graph Neural Networks

arXiv: https://arxiv.org/abs/2003.11702 · HTML: https://mlsanity.com/paper/2003.11702/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Mar 2020.

## Built on by (most cited first, 27 of 27)

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- [A Review of Graph Neural Networks and Their Applications in Power Systems](https://mlsanity.com/paper/2101.10025/) (2021)
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- [Finding the Missing-half: Graph Complementary Learning for Homophily-prone and Heterophily-prone Graphs](https://mlsanity.com/paper/2306.07608/) (2023)
- [How Universal Polynomial Bases Enhance Spectral Graph Neural Networks: Heterophily, Over-smoothing, and Over-squashing](https://mlsanity.com/paper/2405.12474/) (2024)
- [How Expressive are Transformers in Spectral Domain for Graphs?](https://mlsanity.com/paper/2201.09332/) (2022)
- [RA-GCN: Graph Convolutional Network for Disease Prediction Problems with Imbalanced Data](https://mlsanity.com/paper/2103.00221/) (2021)
- [Beyond Low-pass Filtering: Graph Convolutional Networks with Automatic Filtering](https://mlsanity.com/paper/2107.04755/) (2021)
- [Redesigning graph filter-based GNNs to relax the homophily assumption](https://mlsanity.com/paper/2409.08676/) (2024)
- [Multiplex Graph Networks for Multimodal Brain Network Analysis](https://mlsanity.com/paper/2108.00158/) (2021)
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- [Rethinking Spectral Graph Neural Networks with Spatially Adaptive Filtering](https://mlsanity.com/paper/2401.09071/) (2024)
- [Demystifying Higher-Order Graph Neural Networks](https://mlsanity.com/paper/2406.12841/) (2024)
- [Adaptive Filters in Graph Convolutional Neural Networks](https://mlsanity.com/paper/2105.10377/) (2021)
- [Which Hyperparameters to Optimise? An Investigation of Evolutionary Hyperparameter Optimisation in Graph Neural Network For Molecular Property Prediction](https://mlsanity.com/paper/2104.06046/) (2021)
- [Graph Neural Networks in Intelligent Transportation Systems: Advances, Applications and Trends](https://mlsanity.com/paper/2401.00713/) (2024)
- [Nonlinear Laplacians Improve Signed-Directed Graph Learning](https://mlsanity.com/paper/2608.00836/) (2026)
- [Stratified Graph Spectra](https://mlsanity.com/paper/2201.03696/) (2022)
- [An Effective Universal Polynomial Basis for Spectral Graph Neural Networks](https://mlsanity.com/paper/2311.18177/) (2023)
- [Line Graph Vietoris-Rips Persistence Diagram for Topological Graph Representation Learning](https://mlsanity.com/paper/2412.17468/) (2024)
- [Introduction to Graph Neural Networks for Machine Learning Engineers](https://mlsanity.com/paper/2412.19419/) (2024)
- [MF-GCN: A Multi-Frequency Graph Convolutional Network for Tri-Modal Depression Detection Using Eye-Tracking, Facial, and Acoustic Features](https://mlsanity.com/paper/2511.15675/) (2025)
- [Graph Learning Should Move Beyond Restrictive Views of Spectral and Message-Passing GNNs](https://mlsanity.com/paper/2602.10031/) (2026)
- [Controlled Dynamics Attractor Transformer](https://mlsanity.com/paper/2606.15207/) (2026)
- [PANDA: Prior-guided Attentional Dual-path Architecture](https://mlsanity.com/paper/2610.13635/) (2026)

## Abstract (arXiv)

This paper aims at revisiting Graph Convolutional Neural Networks by bridging the gap between spectral and spatial design of graph convolutions. We theoretically demonstrate some equivalence of the graph convolution process regardless it is designed in the spatial or the spectral domain. The obtained general framework allows to lead a spectral analysis of the most popular ConvGNNs, explaining their performance and showing their limits. Moreover, the proposed framework is used to design new convolutions in spectral domain with a custom frequency profile while applying them in the spatial domain. We also propose a generalization of the depthwise separable convolution framework for graph convolutional networks, what allows to decrease the total number of trainable parameters by keeping the capacity of the model. To the best of our knowledge, such a framework has never been used in the GNNs literature. Our proposals are evaluated on both transductive and inductive graph learning problems. Obtained results show the relevance of the proposed method and provide one of the first experimental evidence of transferability of spectral filter coefficients from one graph to another. Our source codes are publicly available at: https://github.com/balcilar/Spectral-Designed-Graph-Convolutions