# A Topology-aware Graph Coarsening Framework for Continual Graph Learning

arXiv: https://arxiv.org/abs/2401.03077 · HTML: https://mlsanity.com/paper/2401.03077/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 63 references that are in the map.
- First posted on arXiv 5 Jan 2024.

## Builds on (most cited first, 30 of 41)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Progressive Neural Networks](https://mlsanity.com/paper/1606.04671/) (2016)
- [Continual Lifelong Learning with Neural Networks: A Review](https://mlsanity.com/paper/1802.07569/) (2018)
- [Experience Replay for Continual Learning](https://mlsanity.com/paper/1811.11682/) (2018)
- [Efficient Lifelong Learning with A-GEM](https://mlsanity.com/paper/1812.00420/) (2018)
- [Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence](https://mlsanity.com/paper/1801.10112/) (2018)
- [Image-based Recommendations on Styles and Substitutes](https://mlsanity.com/paper/1506.04757/) (2015)
- [Lifelong Learning with Dynamically Expandable Networks](https://mlsanity.com/paper/1708.01547/) (2017)
- [Three scenarios for continual learning](https://mlsanity.com/paper/1904.07734/) (2019)
- [Ups and Downs: Modeling the Visual Evolution of Fashion Trends with One-Class Collaborative Filtering](https://mlsanity.com/paper/1602.01585/) (2016)
- [Self-Attention Graph Pooling](https://mlsanity.com/paper/1904.08082/) (2019)
- [Adversarial Attacks on Neural Networks for Graph Data](https://mlsanity.com/paper/1805.07984/) (2018)
- [On Tiny Episodic Memories in Continual Learning](https://mlsanity.com/paper/1902.10486/) (2019)
- [Learning to Remember: A Synaptic Plasticity Driven Framework for Continual Learning](https://mlsanity.com/paper/1904.03137/) (2019)
- [Adversarial Attack and Defense on Graph Data: A Survey](https://mlsanity.com/paper/1812.10528/) (2018)
- [Metrics for Multi-Class Classification: an Overview](https://mlsanity.com/paper/2008.05756/) (2020)
- [A Neural Dirichlet Process Mixture Model for Task-Free Continual Learning](https://mlsanity.com/paper/2001.00689/) (2020)
- [Continual Deep Learning by Functional Regularisation of Memorable Past](https://mlsanity.com/paper/2004.14070/) (2020)
- [Uncertainty-guided Continual Learning with Bayesian Neural Networks](https://mlsanity.com/paper/1906.02425/) (2019)
- [Overcoming Catastrophic Forgetting in Graph Neural Networks](https://mlsanity.com/paper/2012.06002/) (2020)
- [Streaming Graph Neural Networks](https://mlsanity.com/paper/1810.10627/) (2018)
- [Scaling Up Graph Neural Networks Via Graph Coarsening](https://mlsanity.com/paper/2106.05150/) (2021)
- [Streaming Graph Neural Networks via Continual Learning](https://mlsanity.com/paper/2009.10951/) (2020)
- [GraphZoom: A multi-level spectral approach for accurate and scalable graph embedding](https://mlsanity.com/paper/1910.02370/) (2019)
- [Life-Long Disentangled Representation Learning with Cross-Domain Latent Homologies](https://mlsanity.com/paper/1808.06508/) (2018)
- [GraphSAIL: Graph Structure Aware Incremental Learning for Recommender Systems](https://mlsanity.com/paper/2008.13517/) (2020)
- [Graph Coarsening with Preserved Spectral Properties](https://mlsanity.com/paper/1802.04447/) (2018)

## Built on by (most cited first, 11 of 11)

- [When Continue Learning Meets Multimodal Large Language Model: A Survey](https://mlsanity.com/paper/2503.01887/) (2025)
- [Federated Continual Graph Learning](https://mlsanity.com/paper/2411.18919/) (2024)
- [Graph Memory Learning: Imitating Lifelong Remembering and Forgetting of Brain Networks](https://mlsanity.com/paper/2407.19183/) (2024)
- [EC-LDA : Label Distribution Inference Attack against Federated Graph Learning with Embedding Compression](https://mlsanity.com/paper/2505.15140/) (2025)
- [HERO: Preserving Structure and Semantics in Heterogeneous Continual Graph Learning](https://mlsanity.com/paper/2505.17458/) (2025)
- [A Spectral Framework for Evaluating Geodesic Distances Between Graphs](https://mlsanity.com/paper/2406.10500/) (2024)
- [An End-to-End Differentiable, Graph Neural Network-Embedded Pore Network Model for Permeability Prediction](https://mlsanity.com/paper/2509.13841/) (2025)
- [Towards Pre-trained Graph Condensation via Optimal Transport](https://mlsanity.com/paper/2509.14722/) (2025)
- [Scalable Topology-Preserving Graph Coarsening: Concepts and Algorithms](https://mlsanity.com/paper/2601.22943/) (2026)
- [DRIFT: A Benchmark for Task-Free Continual Graph Learning with Continuous Distribution Shifts](https://mlsanity.com/paper/2605.12998/) (2026)
- [SAOT: Self-Supervised Continual Graph Learning with Structure-Aware Optimal Transport](https://mlsanity.com/paper/2607.00377/) (2026)

## Abstract (arXiv)

Continual learning on graphs tackles the problem of training a graph neural network (GNN) where graph data arrive in a streaming fashion and the model tends to forget knowledge from previous tasks when updating with new data. Traditional continual learning strategies such as Experience Replay can be adapted to streaming graphs, however, these methods often face challenges such as inefficiency in preserving graph topology and incapability of capturing the correlation between old and new tasks. To address these challenges, we propose TAmathbbCO, a (t)opology-(a)ware graph (co)arsening and (co)ntinual learning framework that stores information from previous tasks as a reduced graph. At each time period, this reduced graph expands by combining with a new graph and aligning shared nodes, and then it undergoes a "zoom out" process by reduction to maintain a stable size. We design a graph coarsening algorithm based on node representation proximities to efficiently reduce a graph and preserve topological information. We empirically demonstrate the learning process on the reduced graph can approximate that of the original graph. Our experiments validate the effectiveness of the proposed framework on three real-world datasets using different backbone GNN models.