mlsanityData to 7 Oct 2026

Scalable Implicit Graphon Learning

arXiv 2410.17464 ↗First posted 22 Oct 2024stat.ML cs.LGcited by 8

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Abstract (arXiv)

Graphons are continuous models that represent the structure of graphs and allow the generation of graphs of varying sizes. We propose Scalable Implicit Graphon Learning (SIGL), a scalable method that combines implicit neural representations (INRs) and graph neural networks (GNNs) to estimate a graphon from observed graphs. Unlike existing methods, which face important limitations like fixed resolution and scalability issues, SIGL learns a continuous graphon at arbitrary resolutions. GNNs are used to determine the correct node ordering, improving graph alignment. Furthermore, we characterize the asymptotic consistency of our estimator, showing that more expressive INRs and GNNs lead to consistent estimators. We evaluate SIGL in synthetic and real-world graphs, showing that it outperforms existing methods and scales effectively to larger graphs, making it ideal for tasks like graph data augmentation.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Builds on 20 of its 46 references that are in the map. First posted on arXiv 22 Oct 2024.

Builds on

20 of 46 references.

References · 20

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  2. 2017mixup: Beyond Empirical Risk Minimizationcited by 5,155
  3. 2019A Comprehensive Survey on Graph Neural Networkscited by 2,906
  4. 2020Implicit Neural Representations with Periodic Activation Functionscited by 2,214
  5. 2022G-Mixup: Graph Data Augmentation for Graph Classificationcited by 145
  6. 2019Scalable Gromov-Wasserstein Learning for Graph Partitioning and Matchingcited by 102
  7. 2022Signal Processing for Implicit Neural Representationscited by 46
  8. 2013Stochastic blockmodel approximation of a graphon: Theory and consistent estimationcited by 38
  9. 2020Graphon Signal Processingcited by 37
  10. 2014A Consistent Histogram Estimator for Exchangeable Graph Modelscited by 36
  11. 2020Learning Graphons via Structured Gromov-Wasserstein Barycenterscited by 36
  12. 2021Link Scheduling using Graph Neural Networkscited by 26
8 more
  1. 2022Implicit Graphon Neural Representationcited by 18
  2. 2015Private Graphon Estimation for Sparse Graphscited by 17
  3. 2017Centrality measures for graphons: Accounting for uncertainty in networkscited by 17
  4. 2022GraphMAD: Graph Mixup for Data Augmentation using Data-Driven Convex Clusteringcited by 13
  5. 2018Graphon Control of Large-scale Networks of Linear Systemscited by 11
  6. 2020Network Topology Inference with Graphon Spectral Penaltiescited by 11
  7. 2022Joint Network Topology Inference via a Shared Graphon Modelcited by 11
  8. 2024GraSSRep: Graph-Based Self-Supervised Learning for Repeat Detection in Metagenomic Assemblycited by 3

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 4; 2026: 4.

8 papers.

  1. 2025A Few Moments Please: Scalable Graphon Learning via Moment Matchingcited by 3
  2. 2026Prior-Informed Flow Matching for Graph Reconstructioncited by 3
  3. 2025Transfer Learning on Edge Connecting Probability Estimation under Graphon Modelcited by 1
  4. 2026DiPhon: Diffusion on Graphons for Scalable Graph Generationcited by 1
  5. 2025Model-Driven Graph Contrastive Learningcited by 0
  6. 2025From Moments to Models: Graphon-Mixture Learning for Mixup and Contrastive Learningcited by 0
  7. 2026Low-Complexity and Consistent Graphon Estimation from Multiple Networkscited by 0
  8. 2026Feasible Flow Matching for Graph Reconstruction via Within-Sampling Primal-Dual Guidancecited by 0