# Topology Adaptive Graph Convolutional Networks

arXiv: https://arxiv.org/abs/1710.10370 · HTML: https://mlsanity.com/paper/1710.10370/

## Key facts

- Cited by 113 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Oct 2017.

## Built on by (most cited first, 30 of 113)

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- [On the Robustness of Graph Neural Diffusion to Topology Perturbations](https://mlsanity.com/paper/2209.07754/) (2022)
- [Distilling Holistic Knowledge with Graph Neural Networks](https://mlsanity.com/paper/2108.05507/) (2021)
- [Teacher-Student Architecture for Knowledge Distillation: A Survey](https://mlsanity.com/paper/2308.04268/) (2023)
- [Curvature Graph Neural Network](https://mlsanity.com/paper/2106.15762/) (2021)
- [Bending Graphs: Hierarchical Shape Matching using Gated Optimal Transport](https://mlsanity.com/paper/2202.01537/) (2022)
- [Adversarial Robustness in Graph Neural Networks: A Hamiltonian Approach](https://mlsanity.com/paper/2310.06396/) (2023)
- [ReLM: Leveraging Language Models for Enhanced Chemical Reaction Prediction](https://mlsanity.com/paper/2310.13590/) (2023)
- [Optimization-Based Algebraic Multigrid Coarsening Using Reinforcement Learning](https://mlsanity.com/paper/2106.01854/) (2021)
- [Hyper Meta-Path Contrastive Learning for Multi-Behavior Recommendation](https://mlsanity.com/paper/2109.02859/) (2021)
- [Segmentation and Vascular Vectorization for Coronary Artery by Geometry-based Cascaded Neural Network](https://mlsanity.com/paper/2305.04208/) (2023)
- [PowerFlowNet: Power Flow Approximation Using Message Passing Graph Neural Networks](https://mlsanity.com/paper/2311.03415/) (2023)
- [High Fidelity 3D Hand Shape Reconstruction via Scalable Graph Frequency Decomposition](https://mlsanity.com/paper/2307.05541/) (2023)
- [Unleashing the Potential of Fractional Calculus in Graph Neural Networks with FROND](https://mlsanity.com/paper/2404.17099/) (2024)
- [Defending Graph Convolutional Networks against Dynamic Graph Perturbations via Bayesian Self-supervision](https://mlsanity.com/paper/2203.03762/) (2022)
- [Benchmarking Pretrained Molecular Embedding Models For Molecular Representation Learning](https://mlsanity.com/paper/2508.06199/) (2025)
- [Robust Node Classification on Graphs: Jointly from Bayesian Label Transition and Topology-based Label Propagation](https://mlsanity.com/paper/2208.09779/) (2022)
- [MG-GNN: Multigrid Graph Neural Networks for Learning Multilevel Domain Decomposition Methods](https://mlsanity.com/paper/2301.11378/) (2023)
- [MANTRA: The Manifold Triangulations Assemblage](https://mlsanity.com/paper/2410.02392/) (2024)
- [Predicting Basin Stability of Power Grids using Graph Neural Networks](https://mlsanity.com/paper/2108.08230/) (2021)
- [Learning Interface Conditions in Domain Decomposition Solvers](https://mlsanity.com/paper/2205.09833/) (2022)
- [A Survey on Malware Detection with Graph Representation Learning](https://mlsanity.com/paper/2303.16004/) (2023)
- [S3M: Scalable Statistical Shape Modeling through Unsupervised Correspondences](https://mlsanity.com/paper/2304.07515/) (2023)
- [Temporal Graph ODEs for Irregularly-Sampled Time Series](https://mlsanity.com/paper/2404.19508/) (2024)
- [PolyGNN: Polyhedron-based Graph Neural Network for 3D Building Reconstruction from Point Clouds](https://mlsanity.com/paper/2307.08636/) (2023)
- [A Metadata-Driven Approach to Understand Graph Neural Networks](https://mlsanity.com/paper/2310.19263/) (2023)
- [Coupling Graph Neural Networks with Fractional Order Continuous Dynamics: A Robustness Study](https://mlsanity.com/paper/2401.04331/) (2024)
- [A Graphical Approach to Document Layout Analysis](https://mlsanity.com/paper/2308.02051/) (2023)

## Abstract (arXiv)

Spectral graph convolutional neural networks (CNNs) require approximation to the convolution to alleviate the computational complexity, resulting in performance loss. This paper proposes the topology adaptive graph convolutional network (TAGCN), a novel graph convolutional network defined in the vertex domain. We provide a systematic way to design a set of fixed-size learnable filters to perform convolutions on graphs. The topologies of these filters are adaptive to the topology of the graph when they scan the graph to perform convolution. The TAGCN not only inherits the properties of convolutions in CNN for grid-structured data, but it is also consistent with convolution as defined in graph signal processing. Since no approximation to the convolution is needed, TAGCN exhibits better performance than existing spectral CNNs on a number of data sets and is also computationally simpler than other recent methods.