Graphon Theory

Latest papers

9 papers2 papers in the last four weeks, with none the four weeks before. 0.0% of all new papers.

A Generative Model of Complex Networks Using Graphons and Neural Inverse Operators
Oct 1, 2026Wooseong Choi, Italo'Ivo Lima Dias Pinto, Chen Sun +3Graphon Theory Graph Generation
Department of Biomedical Engineering University of Southern California Los Angeles, CA 90089 · Department of Electrical Engineering University of Southern California Los Angeles, CA 90089 · AWS AI Santa Clara, CA 95050
Attention Graphons: A Graph Limit Perspective on Graph Transformers
Sep 28, 2026Caio F. Deberaldini Netto, Moshe Eliasof, Luana RuizGraphon Theory Transformer Attention
Johns Hopkins University Baltimore, MD · University of Cambridge Cambridge, UK
DiPhon: Diffusion on Graphons for Scalable Graph Generation
Jul 8, 2026Sergio Rozada, Yiming Qin, Manuel Madeira +2Graphon Theory Graph Generation
King Juan Carlos University · EPFL, Lausanne, Switzerland · University of Pennsylvania
Zero-Shot Size Transfer for Neural ODEs on Sparse Random Graphs: Graphon Limits and Adjoint Convergence
Jun 25, 2026Mingsong Yan, Zhida Wang, Sui TangGraphon Theory OOD Generalization
Department of Mathematics, University of California, Santa Barbara, CA.
A Topological Characterization of Graph Neural Networks via Stochastic Block Model Embeddings on the n-Sphere
May 29, 2026Gopal AnantharamanGraphon Theory Graph Neural Networks
KnotTheory.ai Inc. · Dept. of Mathematics, Emporia State University
When Do Graph Foundation Models Transfer? A Data-Centric Theory
May 28, 2026Jiajun Zhu, Ying Chen, Peihao Wang +4Graph Positional Encoding Graphon Theory
University of Texas at Austin · Arizona State University · Georgia Institute of Technology
Intensity Dot Product Graphs
Apr 9, 2026Giulio Valentino Dalla Riva, Matteo Dalla RivaGraphon Theory Latent Variable Models
Baffelan OU, Noumea, New Caledonia · Dipartimento di Tecnica e Gestione dei Sistemi Industriali, Università di Padova, Vicenza, Italy
A Note on Graphon-Signal Analysis of Graph Neural Networks
Aug 25, 2025Levi Rauchwerger, Ron LevieGraphon Theory Graph Neural Networks
Graphons of Line Graphs
Sep 3, 2024Sevvandi Kandanaarachchi, Cheng Soon OngGraphon Theory

Oct 1, 2026J/K move · Enter open · S save

A Generative Model of Complex Networks Using Graphons and Neural Inverse Operators

Wooseong Choi, Italo'Ivo Lima Dias Pinto, Chen Sun, Gaurav Gupta+2

Department of Biomedical Engineering University of Southern California Los Angeles, CA 90089 · Department of Electrical Engineering University of Southern California Los Angeles, CA 90089 · AWS AI Santa Clara, CA 95050

Graphon Theory Graph Generation

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Generative graph models are central to understanding and simulating complex networks. However, existing approaches have complementary strengths and limitations. Mechanistic models offer interpretability but rely on instance-specific estimation methods. Deep generative models, on the other hand, offer amortized inference at the cost of interpretability and are largely limited to graph sizes seen during training. Scientific applications motivate a framework that retains the strengths of both paradigms. We bridge them by formulating both the generative model and parameter recovery in function space. A multifractal step graphon extends standard step graphons with a recursive construction that compactly parameterizes complex networks. This formulation admits a neural inverse operator to recover its parameters, enabling inference on unseen graph sizes. We evaluate our model, trained only on synthetic multifractal step graphon realizations, against both paradigms. Against a graph foundation model pretrained on empirical networks, our method achieves the best average performance on three of four metrics in a zero-shot graph-generation benchmark, indicating that the model transfers to real-world graphs. We also apply our method to single-observation networks, a regime largely inaccessible to deep models that require training corpora, where it performs comparably to an instance-specific method that optimizes on each graph. In a multi-subject EEG case study, the inferred parameters track a reversible change in brain state more sensitively than traditional network statistics. Together, these results indicate that mechanistic interpretability and amortized inference can be effectively unified in a generative graph model to enhance our understanding of complex networks.