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# [Awesome-Graph-Reduction](https://github.com/Emory-Melody/awesome-graph-reduction)

[IJCAI 2024] [[A Comprehensive Survey on Graph Reduction: Sparsification, Coarsening, and Condensation]](https://arxiv.org/abs/2402.03358)

<div align=center><img src="https://github.com/ChandlerBang/awesome-graph-reduction/blob/main/figs/graph_reduction.png" width="500" /></div>

Compared to graph sampling and graph algorithm acceleration, graph reduction emphasizes techniques that produce static, model-agnostic and significantly smaller datasets while maintaining high utility.

## Graph Condensation / Graph Dataset Distillation

- [ICML 2024] Graph Condensation via Eigenbasis Matching. [[pdf]](https://arxiv.org/pdf/2310.09202.pdf)
- [ICLR 2024] Mirage: Model-Agnostic Graph Distillation for Graph Classification. [[pdf]](https://openreview.net/pdf?id=78iGZdqxYY) [[code]](https://github.com/idea-iitd/Mirage)
- [arXiv 2024] Simple Graph Condensation. [[pdf]](https://arxiv.org/pdf/2403.14951.pdf)
- [arXiv 2024] Graph Data Condensation via Self-expressive Graph Structure Reconstruction. [[pdf]](https://arxiv.org/pdf/2403.07294v1.pdf) [[code]](https://www.dropbox.com/scl/fi/2aonyp5ln5gisdqtjimu8/GCSR.zip?rlkey=11cuwfpsf54wxiiktu0klud0x&dl=0)
- [ICML 2024] Navigating Complexity: Toward Lossless Graph Condensation via Expanding Window Matching. [[pdf]](https://arxiv.org/pdf/2402.05011.pdf) [[code]](https://github.com/NUS-HPC-AI-Lab/GEOM)
- [arXiv 2024] Two Trades is not Baffled: Condensing Graph via Crafting Rational Gradient Matching [[pdf]](https://arxiv.org/pdf/2402.04924.pdf) [[code]](https://github.com/NUS-HPC-AI-Lab/CTRL)
- [arXiv 2024] Disentangled Condensation for Large-scale Graphs. [[pdf]](https://arxiv.org/pdf/2401.12231.pdf) [[code]](https://github.com/BangHonor/DisCo)
- [TKDE 2024] Heterogeneous Graph Condensation. [[pdf]](https://ieeexplore.ieee.org/abstract/document/10423255) [[code]](https://github.com/jianjianGJ/hgcond)
- [WWW 2024] Globally Interpretable Graph Learning via Distribution Matching. [[pdf]](https://arxiv.org/abs/2306.10447)
- [WWW 2024] EXGC: Bridging Efficiency and Explainability in Graph Condensation. [[pdf]](https://arxiv.org/pdf/2402.05962.pdf) [[code]](https://github.com/MangoKiller/EXGC)
- [WWW 2024] Fast Graph Condensation with Structure-based Neural Tangent Kernel. [[pdf]](https://arxiv.org/pdf/2310.11046.pdf) [[code]](https://github.com/WANGLin0126/GCSNTK)
- [ICDE 2024] Graph Condensation for Inductive Node Representation Learning. [[pdf]](https://arxiv.org/pdf/2307.15967)
- [arXiv 2023] Attend Who is Weak: Enhancing Graph Condensation via Cross-Free Adversarial Training. [[pdf]](https://arxiv.org/pdf/2311.15772.pdf)
- [arXiv 2023] PUMA: Efficient Continual Graph Learning with Graph Condensation. [[pdf]](https://arxiv.org/pdf/2312.14439) [[code]](https://github.com/superallen13/puma)
- [arXiv 2023] Faster Hyperparameter Search for GNNs via Calibrated Dataset Condensation. [[pdf]](https://openreview.net/pdf?id=ohQPU2G3r3C)
- [arXiv 2022] Graph Condensation via Receptive Field Distribution Matching. [[pdf]](https://arxiv.org/pdf/2206.13697.pdf)
- [arXiv 2023] (App) FedGKD: Unleashing the Power of Collaboration in Federated Graph Neural Networks. [[pdf]](https://arxiv.org/pdf/2309.09517.pdf)
- [Applied Sciences 2023] GCARe: Mitigating Subgroup Unfairness in Graph Condensation through Adversarial Regularization. [[pdf]](https://www.mdpi.com/2076-3417/13/16/9166)
- [NeurIPS 2023] Fair Graph Distillation. [[pdf]](https://openreview.net/pdf?id=xW0ayZxPWs)
- [NeurIPS 2023] Structure-free Graph Condensation: From Large-scale Graphs to Condensed Graph-free Data. [[pdf]](https://arxiv.org/pdf/2306.02664.pdf) [[code]](https://github.com/Amanda-Zheng/SFGC)
- [NeurIPS 2023] Does Graph Distillation See Like Vision Dataset Counterpart? [[pdf]](https://openreview.net/pdf?id=VqIWgUVsXc) [[code]](https://github.com/RingBDStack/SGDD)
- [ICDM 2023] CaT: Balanced Continual Graph Learning with Graph Condensation. [[pdf]](https://arxiv.org/pdf/2309.09455.pdf) [[code]](https://github.com/superallen13/CaT-CGL)
- [KDD 2023] Kernel Ridge Regression-Based Graph Dataset Distillation. [[pdf]](https://dl.acm.org/doi/10.1145/3580305.3599398)
- [KBS 2023] Multiple sparse graphs condensation. [[pdf]](https://www.sciencedirect.com/science/article/pii/S0950705123006548) [[code]](https://github.com/jianjianGJ/MSGC)
- [KDD 2022] Condensing Graphs via One-Step Gradient Matching. [[pdf]](https://dl.acm.org/doi/pdf/10.1145/3534678.3539429) [[code]](https://github.com/ChandlerBang/GCond)
- [ICLR 2022] Graph Condensation for Graph Neural Networks. [[pdf]](https://openreview.net/forum?id=WLEx3Jo4QaB) [[code]](https://github.com/ChandlerBang/GCond)

## Graph Coarsening / Clustering / Summary

### GNN-involved

- [ICASSP 2024] Enhancing Performance of Coarsened Graphs with Gradient-Matching. [[pdf]](https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10448089)
- [WWW 2024] Graph-Skeleton: ～ 1% Nodes are Sufficient to Represent Billion-Scale Graph. [[pdf]](https://arxiv.org/pdf/2402.09565.pdf) [[code]](https://github.com/caolinfeng/GraphSkeleton)
- [Pacific Symposium on Biocomputing 2023] A Graph Coarsening Algorithm for Compressing Representations of Single-Cell
Data with Clinical or Experimental Attributes [[pdf]](https://psb.stanford.edu/psb-online/proceedings/psb23/chen_c.pdf) [[code]](https://github.com/ChenCookie/cytocoarsening)
- [arXiv 2023] Graph Coarsening via Convolution Matching for Scalable Graph Neural Network Training. [[pdf]](https://arxiv.org/pdf/2312.15520.pdf) [[code]](https://github.com/amazon-science/convolution-matching)
- [arXiv 2023] ResolvNet: A Graph Convolutional Network with multi-scale Consistency. [[pdf]](https://arxiv.org/pdf/2310.00431.pdf)
- [ICML 2023] Featured Graph Coarsening with Similarity Guarantees. [[pdf]](http://proceedings.mlr.press/v202/kumar23a/kumar23a.pdf)
- [JMLR 2023] A Unified Framework for Optimization-Based Graph Coarsening. [[pdf]](https://www.jmlr.org/papers/volume24/22-1085/22-1085.pdf) [[code]](https://github.com/GraphCoarsening/Featured-Graph-Coarsening)
- [ICLR 2023] Serving Graph Compression for Graph Neural Networks. [[pdf]](https://openreview.net/pdf?id=T-qVtA3pAxG)
- [WWW 2022] (App) ALLIE: Active Learning on Large-scale Imbalanced Graphs. [[pdf]](https://dl.acm.org/doi/pdf/10.1145/3485447.3512229)
- [NeurIPS 2022] (App) SizeShiftReg: a Regularization Method for Improving Size-Generalization in Graph Neural Networks. [[pdf]](https://proceedings.neurips.cc/paper_files/paper/2022/file/ceeb3fa5be458f08fbb12a5bb783aac8-Paper-Conference.pdf) [[code]](https://github.com/DavideBuffelli/SizeShiftReg)
- [WWWc 2022] Scaling R-GCN Training with Graph Summarization. [[pdf]](https://arxiv.org/pdf/2203.02622.pdf)
- [ICLR 2021] Graph Coarsening with Neural Networks. [[pdf]](https://openreview.net/pdf?id=uxpzitPEooJ) [[blog]](https://iclr-blog-track.github.io/2022/03/25/coarsening/)
- [KDD 2021] Scaling Up Graph Neural Networks Via Graph Coarsening. [[pdf]](https://arxiv.org/pdf/2106.05150.pdf) [[code]](https://github.com/szzhang17/Scaling-Up-Graph-Neural-Networks-Via-Graph-Coarsening)
- [HiPC 2021] (App) DistMILE: A Distributed Multi-Level Framework for Scalable Graph Embedding. [[pdf]](https://ieeexplore.ieee.org/document/9680339)
- [ICWSM 2021] (App) MILE: A Multi-Level Framework for Scalable Graph Embedding. [[pdf]](https://arxiv.org/abs/1802.09612) [[code]](https://github.com/jiongqian/MILE)
- [ICLR 2021] Optimization-Based Algebraic Multigrid Coarsening
Using Reinforcement Learning [[pdf]](https://arxiv.org/pdf/2106.01854.pdf) [[code]](https://github.com/compdyn/rl_grid_coarsen)
- [AAAI 2021] Unsupervised Learning of Graph Hierarchical Abstractions with Differentiable Coarsening and Optimal Transport [[pdf]](https://arxiv.org/pdf/1912.11176.pdf) [[code]](https://github.com/matenure/OTCoarsening)
- [ICML 2020] Spectral Clustering with Graph Neural Networks for Graph Pooling. [[pdf]](https://arxiv.org/pdf/1907.00481.pdf) [[code]](https://github.com/FilippoMB/Spectral-Clustering-with-Graph-Neural-Networks-for-Graph-Pooling)
- [KBS 2020] Graph convolutional networks with multi-level coarsening for graph
classification. [[pdf]](https://www.sciencedirect.com/science/article/pii/S0950705120300629)
- [ICML 2020] Learning Algebraic Multigrid Using Graph Neural Networks. [[pdf]](https://proceedings.mlr.press/v119/luz20a/luz20a.pdf) [[code]](https://github.com/ilayluz/learning-amg)
- [ICLR 2020] (App) GraphZoom: A multi-level spectral approach for accurate and scalable graph embedding. [[pdf]](https://arxiv.org/pdf/1910.02370.pdf) [[code]](https://github.com/cornell-zhang/GraphZoom)
- [AAAI 2018] (App) HARP: Hierarchical Representation Learning for Networks. [[pdf]](https://arxiv.org/abs/1706.07845)

### non-GNN-involved

- [AISTATS 2020] Graph Coarsening with Preserved Spectral Properties. [[pdf]](https://arxiv.org/pdf/1802.04447.pdf)
- [NeurIPS 2019] A unifying framework for spectrum-preserving graph sparsification and coarsening. [[pdf]](https://proceedings.neurips.cc/paper_files/paper/2019/file/cd474f6341aeffd65f93084d0dae3453-Paper.pdf) [[code]](https://github.com/TheGravLab/A-Unifying-Framework-for-Spectrum-Preserving-Graph-Sparsification-and-Coarsening)
- [JMLR 2019] Graph reduction with spectral and cut guarantees. [[pdf]](https://arxiv.org/pdf/1808.10650.pdf) [[code]](https://github.com/loukasa/graph-coarsening/tree/v1.1)
- [Chaos 2018] Spectral coarse graining for random walk in bipartite networks. [[pdf]](https://arxiv.org/pdf/1209.1028.pdf)
- [ICML 2018] Spectrally approximating large graphs with smaller graphs. [[pdf]](https://arxiv.org/pdf/1802.07510.pdf)
- [ICDM 2018] NetGist: Learning to Generate Task-Based Network Summaries. [[pdf]](https://faculty.cc.gatech.edu/~badityap/papers/netgist-icdm18.pdf)
- [Signal Processing 2016] (App) A Multiscale Pyramid Transform for Graph Signals. [[pdf]](https://arxiv.org/pdf/1308.4942.pdf)
- [KDD 2014] Fast Influence-based Coarsening for Large Networks. [[pdf]](https://dl.acm.org/doi/pdf/10.1145/2623330.2623701)
- [ICSEE 2014] Graph summarization for attributed graphs. [[pdf]](https://ieeexplore.ieee.org/abstract/document/6948163)
- [arXiv 2013] Aggregation-based aggressive coarsening with polynomial smoothing. [[pdf]](https://arxiv.org/pdf/1307.6305.pdf)
- [SIAM 2012] Lean Algebraic Multigrid (LAMG): Fast Graph Laplacian Linear Solver. [[pdf]](https://arxiv.org/pdf/1108.1310.pdf)
- [SIAM 2011] Relaxation-Based Coarsening and Multiscale Graph Organization. [[pdf]](https://arxiv.org/pdf/1004.1220.pdf)
- [SIAM 2011] Algebraic Distance on Graphs. [[pdf]](https://jiechenjiechen.github.io/pub/algebraic_distance_long.pdf)
- [ICDE 2010] Discovery-driven graph summarization. [[pdf]](https://ieeexplore.ieee.org/abstract/document/5447830)
- [TPAMI 2007] Weighted Graph Cuts without Eigenvectors A Multilevel Approach. [[pdf]](https://ieeexplore.ieee.org/document/4302760)
- [Physical Review E 2005] Coarse-Graining and Self-Dissimilarity of Complex Networks. [[pdf]](https://arxiv.org/pdf/q-bio/0405011.pdf)
- [SIAM 1998] (App) A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs. [[pdf]](https://www.cs.utexas.edu/~pingali/CS395T/2009fa/papers/metis.pdf)
- [Bell System 1970] (App) An efficient heuristic procedure for partitioning graphs [[pdf]](https://ieeexplore.ieee.org/abstract/document/6771089)

## Graph Sparsification / Sampling / Selection

### GNN-involved

- [KDD 2023] Interpretable Sparsification of Brain Graphs: Better Practices and Effective Designs for Graph Neural Networks. [[pdf]](https://dl.acm.org/doi/pdf/10.1145/3580305.3599394) [[code]](https://github.com/motivationss/IGS)
- [TNNLS 2023] (App) Ricci Curvature-Based Graph Sparsification for Continual Graph Representation Learning [[pdf]](https://ieeexplore.ieee.org/document/10225445)
- [NeurIPS 2023] On the Ability of Graph Neural Networks to Model Interactions Between Vertices. [[pdf]](https://arxiv.org/pdf/2211.16494.pdf) [[code]](https://github.com/noamrazin/gnn_interactions)
- [Nature Computational Science 2023] GRAPES: Learning to Sample Graphs for Scalable Graph Neural Networks. [[pdf]](https://www.nature.com/articles/s43588-023-00465-8) [[code]](https://github.com/dfdazac/grapes)
- [ICDM 2022] (App) Sparsified Subgraph Memory for Continual Graph Representation Learning. [[pdf]](https://ieeexplore.ieee.org/document/10027629) [[code]](https://github.com/QueuQ/SSM/issues)
- [ISCA 2022] SmartSAGE: Training Large-scale Graph Neural Networks using In-Storage Processing Architectures. [[pdf]](https://arxiv.org/pdf/2205.04711.pdf)
- [UAI 2022] Principle of Relevant Information for Graph Sparsification. [[pdf]](https://proceedings.mlr.press/v180/yu22c/yu22c.pdf) [[code]](https://github.com/SJYuCNEL/PRI-Graphs)
- [ICLR 2020] GraphSAINT: Graph Sampling Based Inductive Learning Method. [[pdf]](https://arxiv.org/pdf/1907.04931.pdf) [[code]](https://github.com/GraphSAINT/GraphSAINT)
- [ICDM 2020] Graph Sparsification with Generative Adversarial Network. [[pdf]](https://arxiv.org/pdf/2009.11736.pdf)
- [ICML 2020] (App) Robust Graph Representation Learning via Neural Sparsification. [[pdf]](https://proceedings.mlr.press/v119/zheng20d/zheng20d.pdf) [[code]](https://github.com/flyingdoog/PTDNet)
- [TOC 2020] Robust Graph Learning from Noisy Data. [[pdf]](https://arxiv.org/pdf/1812.06673.pdf) [[code]](https://github.com/sckangz/RGC)

### non-GNN-involved

- [STOC 2019] A General Framework for Graph Sparsification. [[pdf]](https://arxiv.org/pdf/1004.4080.pdf)
- [NeurIPS 2019] (Privacy) On Differentially Private Graph Sparsification and Applications. [[pdf]](https://papers.nips.cc/paper_files/paper/2019/file/e44e875c12109e4fa3716c05008048b2-Paper.pdf)
- [AISTATS 2016] Graph Sparsification Approaches for Laplacian Smoothing. [[pdf]](https://www.stat.berkeley.edu/~ryantibs/papers/lapsparse.pdf)
- [Circuits and Systems 2013] Kron Reduction of Graphs with Applications to Electrical Networks. [[pdf]](https://arxiv.org/pdf/1102.2950.pdf)
- [CVPR 2012] Non-negative low rank and sparse graph for semi-supervised learning. [[pdf]](https://zhouchenlin.github.io/Publications/2012-CVPR-NNLRS.pdf)
- [VLDB 2012] Densest Subgraph in Streaming and MapReduce. [[pdf]](https://vldb.org/pvldb/vol5/p454_bahmanbahmani_vldb2012.pdf)
- [VLDB 2012] Dense Subgraph Maintenance under Streaming Edge Weight Updates for Real-time Story Identification. [[pdf]](https://vldb.org/pvldb/vol5/p574_albertangel_vldb2012.pdf)
- [STOC 2011] A General Framework for Graph Sparsification. [[pdf]](https://dl.acm.org/doi/pdf/10.1145/1993636.1993647)
- [STOC 2011] Spectral Sparsification of Graphs [[pdf]](https://epubs.siam.org/doi/abs/10.1137/08074489X)
- [ICDM 2011] Identity Obfuscation in Graphs through the Information Theoretic Lens. [[pdf]](https://ieeexplore.ieee.org/document/5767905)
- [STOC 2008] Graph Sparsification by Effective Resistances. [[pdf]](https://arxiv.org/pdf/0803.0929.pdf)
- [STOC 2004] Nearly-linear time algorithms for graph partitioning, graph sparsification, and solving linear system. [[pdf]](https://dl.acm.org/doi/10.1145/1007352.1007372)
- [Internet Mathematics 2014] Ranking and Sparsifying a Connection Graph. [[pdf]](https://mathweb.ucsd.edu/~fan/wp/connectionj.pdf)
- [ACM 1994] Random sampling in cut, flow, and network design problems. [[pdf]](https://dl.acm.org/doi/pdf/10.1145/195058.195422)
- [JACM 1997] Sparsification–A Technique for Speeding Up Dynamic Graph Algorithms. [[pdf]](https://dl.acm.org/doi/pdf/10.1145/265910.265914)
- [STOC 1996] Approximating s-t minimum cuts in Õ(n2) time. [[pdf]](https://dl.acm.org/doi/pdf/10.1145/237814.237827)
- [STOC 1994] Random sampling in cut, flow, and network design problems. [[pdf]](https://dl.acm.org/doi/10.1145/195058.195422)

## Surveys

Graph Reduction/ Summarization / Simplification

- [IJCAI 2024] A Comprehensive Survey on Graph Reduction: Sparsification, Coarsening, and Condensation. [[pdf]](https://arxiv.org/abs/2402.03358)
- [arXiv 2024] A Survey on Graph Condensation. [[pdf]](https://arxiv.org/abs/2402.02000)
- [arXiv 2024] Graph Condensation: A Survey. [[pdf]](https://arxiv.org/abs/2401.11720)
- [Communications of the ACM] Spectral Sparsification of Graphs: Theory and Algorithms. [[pdf]](http://cs-www.cs.yale.edu/homes/spielman/PAPERS/CACMsparse.pdf)
- [TAI 2023] A Comprehensive Survey on Graph Summarization with Graph Neural Networks. [[pdf]](https://arxiv.org/abs/2302.06114)
- [SeMA 2022] Graph coarsening: from scientific computing to machine learning. [[pdf]](https://link.springer.com/article/10.1007/s40324-021-00282-x)
- [CSR 2020] Multilayer network simplification: Approaches, models and methods [[pdf]](https://arxiv.org/abs/2004.14808)
- [JMLR 2018] Community Detection and Stochastic Block Models: Recent Developments. [[pdf]](https://jmlr.org/papers/volume18/16-480/16-480.pdf)
- [ACS 2018] Graph Summarization Methods and Applications: A Survey. [[pdf]](https://arxiv.org/abs/1612.04883)
- [HPDC 2016] Efficient Processing of Large Graphs via Input Reduction. [[pdf]](https://dl.acm.org/doi/pdf/10.1145/2907294.2907312)
- [VLDB 2005] Densest Subgraph Discovery on Large Graphs: Applications, Challenges, and Techniques. [[pdf]](https://www.vldb.org/pvldb/vol15/p3766-luo.pdf)
- [SIAM 1972] The Transitive Reduction of a Directed Graph. [[pdf]](https://www.cs.tufts.edu/comp/150FP/archive/al-aho/transitive-reduction.pdf)

Other related topics

- [arXiv 2023] Dataset Distillation: A Comprehensive Review. [[pdf]](https://arxiv.org/pdf/2301.07014.pdf)
- [IJCAI 2023] A Survey on Dataset Distillation: Approaches, Applications and Future Directions. [[pdf]](https://arxiv.org/pdf/2305.01975.pdf)

## Toolkits

- Mongoose: [[pdf]](https://people.clas.ufl.edu/hager/files/mongoose.pdf) [[code]](https://github.com/ScottKolo/Mongoose)
- PyGSP: [[code]](https://github.com/epfl-lts2/pygsp)
- graph-tool: [[code]](https://graph-tool.skewed.de/)