# Topological Relational Learning on Graphs

arXiv: https://arxiv.org/abs/2110.15529 · HTML: https://mlsanity.com/paper/2110.15529/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 74 references that are in the map.
- First posted on arXiv 29 Oct 2021.

## Builds on (most cited first, 30 of 40)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View](https://mlsanity.com/paper/1909.03211/) (2019)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [Deep Learning on Graphs: A Survey](https://mlsanity.com/paper/1812.04202/) (2018)
- [Graph Structure Learning for Robust Graph Neural Networks](https://mlsanity.com/paper/2005.10203/) (2020)
- [Adversarial Attack on Graph Structured Data](https://mlsanity.com/paper/1806.02371/) (2018)
- [Towards Deeper Graph Neural Networks](https://mlsanity.com/paper/2007.09296/) (2020)
- [Graph Neural Networks with convolutional ARMA filters](https://mlsanity.com/paper/1901.01343/) (2019)
- [An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists](https://mlsanity.com/paper/1710.04019/) (2017)
- [Adversarial Attack and Defense on Graph Data: A Survey](https://mlsanity.com/paper/1812.10528/) (2018)
- [PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures](https://mlsanity.com/paper/1904.09378/) (2019)
- [Large-Scale Learnable Graph Convolutional Networks](https://mlsanity.com/paper/1808.03965/) (2018)
- [Wasserstein Weisfeiler-Lehman Graph Kernels](https://mlsanity.com/paper/1906.01277/) (2019)
- [Unifying Graph Convolutional Neural Networks and Label Propagation](https://mlsanity.com/paper/2002.06755/) (2020)
- [GMNN: Graph Markov Neural Networks](https://mlsanity.com/paper/1905.06214/) (2019)
- [MotifNet: a motif-based Graph Convolutional Network for directed graphs](https://mlsanity.com/paper/1802.01572/) (2018)
- [Learning metrics for persistence-based summaries and applications for graph classification](https://mlsanity.com/paper/1904.12189/) (2019)
- [N-GCN: Multi-scale Graph Convolution for Semi-supervised Node Classification](https://mlsanity.com/paper/1802.08888/) (2018)
- [Persistence Fisher Kernel: A Riemannian Manifold Kernel for Persistence Diagrams](https://mlsanity.com/paper/1802.03569/) (2018)
- [SPAGAN: Shortest Path Graph Attention Network](https://mlsanity.com/paper/2101.03464/) (2021)
- [Impact of regularization on Spectral Clustering](https://mlsanity.com/paper/1312.1733/) (2013)
- [Nonlinear Higher-Order Label Spreading](https://mlsanity.com/paper/2006.04762/) (2020)
- [Fisher-Bures Adversary Graph Convolutional Networks](https://mlsanity.com/paper/1903.04154/) (2019)

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

- [Large Language Models are Good Relational Learners](https://mlsanity.com/paper/2506.05725/) (2025)
- [Going beyond persistent homology using persistent homology](https://mlsanity.com/paper/2311.06152/) (2023)
- [On the Expressivity of Persistent Homology in Graph Learning](https://mlsanity.com/paper/2302.09826/) (2023)
- [Neural Approximation of Graph Topological Features](https://mlsanity.com/paper/2201.12032/) (2022)
- [TopoGCL: Topological Graph Contrastive Learning](https://mlsanity.com/paper/2406.17251/) (2024)
- [Tensor-view Topological Graph Neural Network](https://mlsanity.com/paper/2401.12007/) (2024)
- [Cycle Invariant Positional Encoding for Graph Representation Learning](https://mlsanity.com/paper/2311.14333/) (2023)
- [Enhancing Graph Representation Learning with Localized Topological Features](https://mlsanity.com/paper/2501.09178/) (2025)
- [RTD-Lite: Scalable Topological Analysis for Comparing Weighted Graphs in Learning Tasks](https://mlsanity.com/paper/2503.11910/) (2025)
- [On topological descriptors for graph products](https://mlsanity.com/paper/2511.08846/) (2025)
- [Reduction Algorithms for Persistence Diagrams of Networks: CoralTDA and PrunIT](https://mlsanity.com/paper/2211.13708/) (2022)
- [PHLP: Sole Persistent Homology for Link Prediction - Interpretable Feature Extraction](https://mlsanity.com/paper/2404.15225/) (2024)
- [Dynamic Neural Dowker Network: Approximating Persistent Homology in Dynamic Directed Graphs](https://mlsanity.com/paper/2408.09123/) (2024)
- [When Witnesses Defend: A Witness Graph Topological Layer for Adversarial Graph Learning](https://mlsanity.com/paper/2409.14161/) (2024)
- [Graph Persistence goes Spectral](https://mlsanity.com/paper/2506.06571/) (2025)
- [Topology Only Pre-Training: Towards Generalised Multi-Domain Graph Models](https://mlsanity.com/paper/2311.03976/) (2023)
- [Relational Learning in Pre-Trained Models: A Theory from Hypergraph Recovery Perspective](https://mlsanity.com/paper/2406.11249/) (2024)
- [CellCLAT: Preserving Topology and Trimming Redundancy in Self-Supervised Cellular Contrastive Learning](https://mlsanity.com/paper/2505.21587/) (2025)
- [TMetaNet: Topological Meta-Learning Framework for Dynamic Link Prediction](https://mlsanity.com/paper/2506.00453/) (2025)
- [Heat Kernel Goes Topological](https://mlsanity.com/paper/2507.12380/) (2025)
- [Privacy-Preserving Representation Learning for Text-Attributed Networks with Simplicial Complexes](https://mlsanity.com/paper/2302.04383/) (2023)
- [Virtual Node Generation for Node Classification in Sparsely-Labeled Graphs](https://mlsanity.com/paper/2409.07712/) (2024)
- [A Metric for the Balance of Information in Graph Learning](https://mlsanity.com/paper/2501.19137/) (2025)
- [Scalable Topology-Preserving Graph Coarsening: Concepts and Algorithms](https://mlsanity.com/paper/2601.22943/) (2026)
- [Weisfeiler Lehman Test on Combinatorial Complexes: Generalized Expressive Power of Topological Neural Networks](https://mlsanity.com/paper/2605.00725/) (2026)
- [Collapsed Effective Operators for Higher-order Structures](https://mlsanity.com/paper/2606.23517/) (2026)
- [Signed Graph Pre-Training and Prompt Learning](https://mlsanity.com/paper/2609.25722/) (2026)

## Abstract (arXiv)

Graph neural networks (GNNs) have emerged as a powerful tool for graph classification and representation learning. However, GNNs tend to suffer from over-smoothing problems and are vulnerable to graph perturbations. To address these challenges, we propose a novel topological neural framework of topological relational inference (TRI) which allows for integrating higher-order graph information to GNNs and for systematically learning a local graph structure. The key idea is to rewire the original graph by using the persistent homology of the small neighborhoods of nodes and then to incorporate the extracted topological summaries as the side information into the local algorithm. As a result, the new framework enables us to harness both the conventional information on the graph structure and information on the graph higher order topological properties. We derive theoretical stability guarantees for the new local topological representation and discuss their implications on the graph algebraic connectivity. The experimental results on node classification tasks demonstrate that the new TRI-GNN outperforms all 14 state-of-the-art baselines on 6 out 7 graphs and exhibit higher robustness to perturbations, yielding up to 10% better performance under noisy scenarios.