# Topological Graph Neural Networks

arXiv: https://arxiv.org/abs/2102.07835 · HTML: https://mlsanity.com/paper/2102.07835/

## Key facts

- Cited by 87 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 65 references that are in the map.
- First posted on arXiv 15 Feb 2021.

## Builds on (most cited first, 30 of 31)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- [Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View](https://mlsanity.com/paper/1909.03211/) (2019)
- [Provably Powerful Graph Networks](https://mlsanity.com/paper/1905.11136/) (2019)
- [Residual Gated Graph ConvNets](https://mlsanity.com/paper/1711.07553/) (2017)
- [Improving Graph Neural Network Expressivity via Subgraph Isomorphism Counting](https://mlsanity.com/paper/2006.09252/) (2020)
- [Can Graph Neural Networks Count Substructures?](https://mlsanity.com/paper/2002.04025/) (2020)
- [On the equivalence between graph isomorphism testing and function approximation with GNNs](https://mlsanity.com/paper/1905.12560/) (2019)
- [A Survey on Graph Kernels](https://mlsanity.com/paper/1903.11835/) (2019)
- [Topological Autoencoders](https://mlsanity.com/paper/1906.00722/) (2019)
- [PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures](https://mlsanity.com/paper/1904.09378/) (2019)
- [Deep Learning with Topological Signatures](https://mlsanity.com/paper/1707.04041/) (2017)
- [Graph Filtration Learning](https://mlsanity.com/paper/1905.10996/) (2019)
- [On Weisfeiler-Leman Invariance: Subgraph Counts and Related Graph Properties](https://mlsanity.com/paper/1811.04801/) (2018)
- [Graph Kernels: State-of-the-Art and Future Challenges](https://mlsanity.com/paper/2011.03854/) (2020)
- [Learning metrics for persistence-based summaries and applications for graph classification](https://mlsanity.com/paper/1904.12189/) (2019)
- [On Valid Optimal Assignment Kernels and Applications to Graph Classification](https://mlsanity.com/paper/1606.01141/) (2016)
- [Graph Kernels: A Survey](https://mlsanity.com/paper/1904.12218/) (2019)
- [Uncovering the Topology of Time-Varying fMRI Data using Cubical Persistence](https://mlsanity.com/paper/2006.07882/) (2020)
- [On the Combinatorial Power of the Weisfeiler-Lehman Algorithm](https://mlsanity.com/paper/1704.01023/) (2017)
- [Continuation of Point Clouds via Persistence Diagrams](https://mlsanity.com/paper/1506.03147/) (2015)
- [PersGNN: Applying Topological Data Analysis and Geometric Deep Learning to Structure-Based Protein Function Prediction](https://mlsanity.com/paper/2010.16027/) (2020)
- [Stabilizing the unstable output of persistent homology computations](https://mlsanity.com/paper/1512.01700/) (2015)

## Built on by (most cited first, 30 of 87)

- [Structure-Aware Transformer for Graph Representation Learning](https://mlsanity.com/paper/2202.03036/) (2022)
- [Weisfeiler and Leman go Machine Learning: The Story so far](https://mlsanity.com/paper/2112.09992/) (2021)
- [Rethinking the Expressive Power of GNNs via Graph Biconnectivity](https://mlsanity.com/paper/2301.09505/) (2023)
- [Position: Topological Deep Learning is the New Frontier for Relational Learning](https://mlsanity.com/paper/2402.08871/) (2024)
- [Ordered Subgraph Aggregation Networks](https://mlsanity.com/paper/2206.11168/) (2022)
- [Evaluation Metrics for Graph Generative Models: Problems, Pitfalls, and Practical Solutions](https://mlsanity.com/paper/2106.01098/) (2021)
- [Beyond Weisfeiler-Lehman: A Quantitative Framework for GNN Expressiveness](https://mlsanity.com/paper/2401.08514/) (2024)
- [Topological Deep Learning: A Review of an Emerging Paradigm](https://mlsanity.com/paper/2302.03836/) (2023)
- [WL meet VC](https://mlsanity.com/paper/2301.11039/) (2023)
- [Is Distance Matrix Enough for Geometric Deep Learning?](https://mlsanity.com/paper/2302.05743/) (2023)
- [Going beyond persistent homology using persistent homology](https://mlsanity.com/paper/2311.06152/) (2023)
- [Embedding in Recommender Systems: A Survey](https://mlsanity.com/paper/2310.18608/) (2023)
- [Curvature Filtrations for Graph Generative Model Evaluation](https://mlsanity.com/paper/2301.12906/) (2023)
- [On the Expressivity of Persistent Homology in Graph Learning](https://mlsanity.com/paper/2302.09826/) (2023)
- [Continual Graph Learning: A Survey](https://mlsanity.com/paper/2301.12230/) (2023)
- [Differentiable Euler Characteristic Transforms for Shape Classification](https://mlsanity.com/paper/2310.07630/) (2023)
- [Simplicial Representation Learning with Neural k-Forms](https://mlsanity.com/paper/2312.08515/) (2023)
- [Affinity-Aware Graph Networks](https://mlsanity.com/paper/2206.11941/) (2022)
- [SGAT: Simplicial Graph Attention Network](https://mlsanity.com/paper/2207.11761/) (2022)
- [Understanding Virtual Nodes: Oversquashing and Node Heterogeneity](https://mlsanity.com/paper/2405.13526/) (2024)
- [GRIL: A 2-parameter Persistence Based Vectorization for Machine Learning](https://mlsanity.com/paper/2304.04970/) (2023)
- [Weisfeiler-Leman at the margin: When more expressivity matters](https://mlsanity.com/paper/2402.07568/) (2024)
- [Tensor-view Topological Graph Neural Network](https://mlsanity.com/paper/2401.12007/) (2024)
- [MANTRA: The Manifold Triangulations Assemblage](https://mlsanity.com/paper/2410.02392/) (2024)
- [Boosting Graph Pooling with Persistent Homology](https://mlsanity.com/paper/2402.16346/) (2024)
- [Adaptive Topological Feature via Persistent Homology: Filtration Learning for Point Clouds](https://mlsanity.com/paper/2307.09259/) (2023)
- [Cycle Invariant Positional Encoding for Graph Representation Learning](https://mlsanity.com/paper/2311.14333/) (2023)
- [Union Subgraph Neural Networks](https://mlsanity.com/paper/2305.15747/) (2023)
- [Diss-l-ECT: Dissecting Graph Data with Local Euler Characteristic Transforms](https://mlsanity.com/paper/2410.02622/) (2024)
- [Enhancing Graph Representation Learning with Localized Topological Features](https://mlsanity.com/paper/2501.09178/) (2025)

## Abstract (arXiv)

Graph neural networks (GNNs) are a powerful architecture for tackling graph learning tasks, yet have been shown to be oblivious to eminent substructures such as cycles. We present TOGL, a novel layer that incorporates global topological information of a graph using persistent homology. TOGL can be easily integrated into any type of GNN and is strictly more expressive (in terms the Weisfeiler--Lehman graph isomorphism test) than message-passing GNNs. Augmenting GNNs with TOGL leads to improved predictive performance for graph and node classification tasks, both on synthetic data sets, which can be classified by humans using their topology but not by ordinary GNNs, and on real-world data.