# Structure-free Graph Condensation: From Large-scale Graphs to Condensed Graph-free Data

arXiv: https://arxiv.org/abs/2306.02664 · HTML: https://mlsanity.com/paper/2306.02664/

## Key facts

- Cited by 71 papers in the map (data through 14 Oct 2026).
- Builds on 61 of its 83 references that are in the map.
- First posted on arXiv 5 Jun 2023.

## Builds on (most cited first, 30 of 61)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [iCaRL: Incremental Classifier and Representation Learning](https://mlsanity.com/paper/1611.07725/) (2016)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Continual Lifelong Learning with Neural Networks: A Review](https://mlsanity.com/paper/1802.07569/) (2018)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [GraphSAINT: Graph Sampling Based Inductive Learning Method](https://mlsanity.com/paper/1907.04931/) (2019)
- [Cluster-GCN: An Efficient Algorithm for Training Deep and Large Graph Convolutional Networks](https://mlsanity.com/paper/1905.07953/) (2019)
- [Dataset Condensation with Gradient Matching](https://mlsanity.com/paper/2006.05929/) (2020)
- [Dataset Distillation by Matching Training Trajectories](https://mlsanity.com/paper/2203.11932/) (2022)
- [Dataset Condensation with Distribution Matching](https://mlsanity.com/paper/2110.04181/) (2021)
- [Graph Self-Supervised Learning: A Survey](https://mlsanity.com/paper/2103.00111/) (2021)
- [Adversarial Attacks on Graph Neural Networks via Meta Learning](https://mlsanity.com/paper/1902.08412/) (2019)
- [Dataset Meta-Learning from Kernel Ridge-Regression](https://mlsanity.com/paper/2011.00050/) (2020)
- [Dataset Distillation with Infinitely Wide Convolutional Networks](https://mlsanity.com/paper/2107.13034/) (2021)
- [Anomaly Detection on Attributed Networks via Contrastive Self-Supervised Learning](https://mlsanity.com/paper/2103.00113/) (2021)
- [Graph Neural Networks for Graphs with Heterophily: A Survey](https://mlsanity.com/paper/2202.07082/) (2022)
- [Graph Neural Tangent Kernel: Fusing Graph Neural Networks with Graph Kernels](https://mlsanity.com/paper/1905.13192/) (2019)
- [Graph-less Neural Networks: Teaching Old MLPs New Tricks via Distillation](https://mlsanity.com/paper/2110.08727/) (2021)
- [Graph Condensation for Graph Neural Networks](https://mlsanity.com/paper/2110.07580/) (2021)
- [Attributed Graph Clustering: A Deep Attentional Embedding Approach](https://mlsanity.com/paper/1906.06532/) (2019)
- [Pre-training of Graph Augmented Transformers for Medication Recommendation](https://mlsanity.com/paper/1906.00346/) (2019)
- [A Unified Lottery Ticket Hypothesis for Graph Neural Networks](https://mlsanity.com/paper/2102.06790/) (2021)
- [A Comprehensive Survey of Dataset Distillation](https://mlsanity.com/paper/2301.05603/) (2023)
- [Towards Unsupervised Deep Graph Structure Learning](https://mlsanity.com/paper/2201.06367/) (2022)

## Built on by (most cited first, 30 of 71)

- [Reasoning on Graphs: Faithful and Interpretable Large Language Model Reasoning](https://mlsanity.com/paper/2310.01061/) (2023)
- [A Comprehensive Survey on Graph Reduction: Sparsification, Coarsening, and Condensation](https://mlsanity.com/paper/2402.03358/) (2024)
- [Towards Self-Interpretable Graph-Level Anomaly Detection](https://mlsanity.com/paper/2310.16520/) (2023)
- [Fast Graph Condensation with Structure-based Neural Tangent Kernel](https://mlsanity.com/paper/2310.11046/) (2023)
- [Navigating Complexity: Toward Lossless Graph Condensation via Expanding Window Matching](https://mlsanity.com/paper/2402.05011/) (2024)
- [PREM: A Simple Yet Effective Approach for Node-Level Graph Anomaly Detection](https://mlsanity.com/paper/2310.11676/) (2023)
- [Graph Condensation: A Survey](https://mlsanity.com/paper/2401.11720/) (2024)
- [Rethinking and Accelerating Graph Condensation: A Training-Free Approach with Class Partition](https://mlsanity.com/paper/2405.13707/) (2024)
- [Data-centric Graph Learning: A Survey](https://mlsanity.com/paper/2310.04987/) (2023)
- [Graph Data Condensation via Self-expressive Graph Structure Reconstruction](https://mlsanity.com/paper/2403.07294/) (2024)
- [GNNEvaluator: Evaluating GNN Performance On Unseen Graphs Without Labels](https://mlsanity.com/paper/2310.14586/) (2023)
- [Graph Distillation with Eigenbasis Matching](https://mlsanity.com/paper/2310.09202/) (2023)
- [Towards Data-centric Graph Machine Learning: Review and Outlook](https://mlsanity.com/paper/2309.10979/) (2023)
- [Online GNN Evaluation Under Test-time Graph Distribution Shifts](https://mlsanity.com/paper/2403.09953/) (2024)
- [GC-Bench: An Open and Unified Benchmark for Graph Condensation](https://mlsanity.com/paper/2407.00615/) (2024)
- [Disentangled Condensation for Large-scale Graphs](https://mlsanity.com/paper/2401.12231/) (2024)
- [PUMA: Efficient Continual Graph Learning for Node Classification with Graph Condensation](https://mlsanity.com/paper/2312.14439/) (2023)
- [A Survey on Graph Condensation](https://mlsanity.com/paper/2402.02000/) (2024)
- [Graph Condensation for Open-World Graph Learning](https://mlsanity.com/paper/2405.17003/) (2024)
- [Graph Coarsening with Message-Passing Guarantees](https://mlsanity.com/paper/2405.18127/) (2024)
- [Two Trades is not Baffled: Condensing Graph via Crafting Rational Gradient Matching](https://mlsanity.com/paper/2402.04924/) (2024)
- [Simple Graph Condensation](https://mlsanity.com/paper/2403.14951/) (2024)
- [Federated Graph Condensation with Information Bottleneck Principles](https://mlsanity.com/paper/2405.03911/) (2024)
- [Learning on Large Graphs using Intersecting Communities](https://mlsanity.com/paper/2405.20724/) (2024)
- [RobGC: Towards Robust Graph Condensation](https://mlsanity.com/paper/2406.13200/) (2024)
- [GCAL: Adapting Graph Models to Evolving Domain Shifts](https://mlsanity.com/paper/2505.16860/) (2025)
- [GC4NC: A Benchmark Framework for Graph Condensation on Node Classification with New Insights](https://mlsanity.com/paper/2406.16715/) (2024)
- [Contrastive Graph Condensation: Advancing Data Versatility through Self-Supervised Learning](https://mlsanity.com/paper/2411.17063/) (2024)
- [Scalable Graph Condensation with Evolving Capabilities](https://mlsanity.com/paper/2502.17614/) (2025)
- [GCondenser: Benchmarking Graph Condensation](https://mlsanity.com/paper/2405.14246/) (2024)

## Abstract (arXiv)

Graph condensation, which reduces the size of a large-scale graph by synthesizing a small-scale condensed graph as its substitution, has immediate benefits for various graph learning tasks. However, existing graph condensation methods rely on the joint optimization of nodes and structures in the condensed graph, and overlook critical issues in effectiveness and generalization ability. In this paper, we advocate a new Structure-Free Graph Condensation paradigm, named SFGC, to distill a large-scale graph into a small-scale graph node set without explicit graph structures, i.e., graph-free data. Our idea is to implicitly encode topology structure information into the node attributes in the synthesized graph-free data, whose topology is reduced to an identity matrix. Specifically, SFGC contains two collaborative components: (1) a training trajectory meta-matching scheme for effectively synthesizing small-scale graph-free data; (2) a graph neural feature score metric for dynamically evaluating the quality of the condensed data. Through training trajectory meta-matching, SFGC aligns the long-term GNN learning behaviors between the large-scale graph and the condensed small-scale graph-free data, ensuring comprehensive and compact transfer of informative knowledge to the graph-free data. Afterward, the underlying condensed graph-free data would be dynamically evaluated with the graph neural feature score, which is a closed-form metric for ensuring the excellent expressiveness of the condensed graph-free data. Extensive experiments verify the superiority of SFGC across different condensation ratios.