#graphons
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mathst-bot.bsky.social
Wei Li, Robert Lunde: Central Limit Theorems and Network-Free Inference for Heterogeneous Spatial Autoregressions on Sparse Graphons https://arxiv.org/abs/2610.40630 https://arxiv.org/pdf/2610.40630 https://arxiv.org/html/2610.40630
October 30, 2026 at 6:51 AM
arxiv-stat-ml.bsky.social
Taeyoung Kim, Jineon Baek, Joonkyung Lee, Hongseok Yang
Implicit Neural Representations for Variational Problems on Graphons
https://arxiv.org/abs/2610.32147
October 27, 2026 at 5:46 AM
paperposterbot.bsky.social
arXiv📈🤖
Central Limit Theorems and Network-Free Inference for Heterogeneous Spatial Autoregressions on Sparse Graphons
By Li, Lunde
Network dependence is widely regarded as a fundamental obstacle to inference: outcomes linked through a graph are not independent, the graph is rarely observed in full, and models for how dependence propagates are easily misspecified. We show that for a broad class of responses generated through a random network, the obstacle is smaller than it appears. We study a heterogeneous spatial autoregression on a sparse graphon, in which each node's response is a weighted average of its neighbors' responses with a node-specific, nonparametric coefficient plus a node-specific input, and we prove that sample means and smooth functions of vector means are asymptotically Gaussian down to average degree nearly logarithmic in the population size, allowing unbounded graphons with hubs and heavy-tailed inputs. The limiting variance interpolates exactly between two regimes according to the sampling fraction. When the observed nodes are a vanishing fraction of the population, the variance is the marginal variance of the response, the ordinary sample variance is consistent, and the usual $t$-interval is valid with no knowledge of the network. The proof averages over the graph rather than conditioning on it, isolating the behavior of the response through an exact identity for resolvents of Markov kernels and controlling the network noise by an Efron-Stein inequality; neither step requires the walk-by-walk covariance bounds of fixed-network analyses. Consequences for regression with node-level and network-derived covariates are derived.
October 30, 2026 at 12:09 PM
statml-bot.bsky.social
Taeyoung Kim, Jineon Baek, Joonkyung Lee, Hongseok Yang: Implicit Neural Representations for Variational Problems on Graphons https://arxiv.org/abs/2610.32147 https://arxiv.org/pdf/2610.32147 https://arxiv.org/html/2610.32147
October 26, 2026 at 7:03 AM
danielcooney1.bsky.social
I am happy to share a new preprint with Daecheol Kim, Yefei Zhang, and Yuxuan Zhao on The Keller-Segel Model for Chemotaxis on Metapopulation Graphs and Graphons.

In this paper, we explore spatial pattern formation through directed motion on patch-structured populations.

arxiv.org/abs/2610.31049
The Keller-Segel Model for Chemotaxis on Metapopulation Graphs and Graphons
Many models of spatial populations use directed motion towards environmental attractants as a mechanism for spatial pattern formation. While prior approaches typically focus on partial differential eq...
arxiv.org
October 23, 2026 at 2:00 PM
mathds-bot.bsky.social
Daecheol Kim, Yefei Zhang, Yuxuan Zhao, Daniel B. Cooney: The Keller-Segel Model for Chemotaxis on Metapopulation Graphs and Graphons https://arxiv.org/abs/2610.31049 https://arxiv.org/pdf/2610.31049 https://arxiv.org/html/2610.31049
October 23, 2026 at 6:47 AM
cslg-bot.bsky.social
Wooseong Choi, Italo'Ivo Lima Dias Pinto, Chen Sun, Gaurav Gupta, Dong Song, Paul Bogdan: A Generative Model of Complex Networks Using Graphons and Neural Inverse Operators https://arxiv.org/abs/2610.02439 https://arxiv.org/pdf/2610.02439 https://arxiv.org/html/2610.02439
October 5, 2026 at 6:42 AM
mathco-bot.bsky.social
Mugdha Mahesh Pokharanakar: Cheeger constants and bipartiteness ratios of Cayley graphons https://arxiv.org/abs/2610.01745 https://arxiv.org/pdf/2610.01745 https://arxiv.org/html/2610.01745
October 2, 2026 at 6:47 AM
cslg-bot.bsky.social
Caio F. Deberaldini Netto, Moshe Eliasof, Luana Ruiz: Attention Graphons: A Graph Limit Perspective on Graph Transformers https://arxiv.org/abs/2609.35620 https://arxiv.org/pdf/2609.35620 https://arxiv.org/html/2609.35620
September 30, 2026 at 6:53 AM
cslg-bot.bsky.social
Caio F. Deberaldini Netto, Moshe Eliasof, Luana Ruiz: Attention Graphons: A Graph Limit Perspective on Graph Transformers https://arxiv.org/abs/2609.35620 https://arxiv.org/pdf/2609.35620 https://arxiv.org/html/2609.35620
September 29, 2026 at 6:53 AM
soc-net-bot.bsky.social
Explicit Bounds on the Entropy of Piecewise H\"{o}lder Graphon Models
https://arxiv.org/abs/2608.26501
We study the entropy of random graphs generated by piecewise H\"{o}lder continuous graphons. We first present a result on the rate of convergence of the normalized entropy as the size of the...📈🤖
August 28, 2026 at 12:38 PM
paperposterbot.bsky.social
arXiv📈🤖
Joint Estimation of Sparse Multilayer Networks via Graph Limits
By Song, Olhede
Network datasets in modern applications often involve multiple types of interactions occurring over a shared set of individuals. Characterizing the generating mechanisms of these interactions can be enhanced by joint modelling, as shared vertices allow layers to help explain the structure of other layers. We model multiplex observations using graph limits, called a scaled set of graphons, and develop a nonparametric joint estimator based on blockmodel approximations, termed the multi-network histogram. This nonparametric framework captures each layer's varying sparsity and connection structure, accounting for heterogeneity via shared latent variables across all layers. We establish the theoretical properties of the multi-network histogram, providing an upper bound for the weighted mean integrated squared error and deriving the optimal bandwidth that minimizes this error. By leveraging information across layers, this joint modelling achieves a reduction in error and a smaller optimal bandwidth, which enables high-resolution estimation even in sparser layers. Its usefulness is demonstrated through simulation studies and an application to socioeconomic networks in an Indian village.
August 17, 2026 at 5:29 PM
aliceernoult.bsky.social
Je découvre dans la lettre d'information de la #CFEM (une véritable mine d'or soit dit en passant), les Snapshots d'@imaginary_math! Dans un article de Tereza Klimošová je découvre par exemple ce que sont les "graphons".

imaginary.org/snapshot/limit…
Limits of graph sequences | IMAGINARY
Graphs are simple mathematical structures used to model a wide variety of real-life objects. With the rise of computers, the size of the graphs used for these models has grown enormously. The need to efficiently represent and study properties of extremely large graphs led to the development of the theory of graph limits.
www.imaginary.org
December 2, 2024 at 8:45 PM
alejandroparadam.bsky.social
A new preprint is out: "RKHS Representation of Algebraic Convolutional Filters with Integral Operators", arxiv.org/abs/2602.19094
RKHS Representation of Algebraic Convolutional Filters with Integral Operators
Integral operators play a central role in signal processing, underpinning classical convolution, and filtering on continuous network models such as graphons. While these operators are traditionally an...
arxiv.org
February 24, 2026 at 3:08 AM
arxiv-math-mp.bsky.social
Bertram D\"uring, Jonathan Franceschi, Marie-Therese Wolfram, Mattia Zanella
Breaking consensus in kinetic opinion formation models on graphons
https://arxiv.org/abs/2403.14431
March 22, 2024 at 5:00 AM
paperposterbot.bsky.social
arXiv📈🤖
Decorated graphons for temporal network estimation
By Dufour, Olhede
We propose a unified nonparametric framework for modeling time-evolving networks using decorated graphons (also known as probability-graphons): symmetric functions that assign to each node pair a probability distribution over binary edge time series. This generalizes the static decorated-graphon construction to dynamic graphs while preserving node exchangeability and allowing temporal dynamics such as memory and periodicity. Models in which edges evolve independently given the latent variables, such as autoregressive and Markov edge processes, arise as special cases. We develop a two-stage estimation procedure that separates temporal modeling from network structure. Because the network stage requires only mild regularity conditions on the edge-process estimator, a broad class of temporal edge models can be used in the first stage. We establish nonparametric convergence rates in both block-model and H\"older-smooth regimes, and make explicit how the rate depends on the number of observed time steps and on the quality of the edge-level estimation. We illustrate the method on simulated data and a hospital contact network, recovering latent community structure and time-varying interaction patterns. The framework gives a nonparametric baseline for dynamic network analysis with explicit convergence guarantees.
July 28, 2026 at 4:38 AM
paperposterbot.bsky.social
arXiv📈🤖
Leave-One-Out Neighborhood Smoothing for Graphons: Berry-Esseen Bounds, Confidence Intervals, and Honest Tuning
By Aalipur, Kilby
Neighborhood smoothing methods achieve minimax-optimal rates for estimating edge probabilities under graphon models, but their use for statistical inference has remained limited. The main obstacle is that classical neighborhood smoothers select data-driven neighborhoods and average edges using the same adjacency matrix, inducing complex dependencies that invalidate standard concentration and normal approximation arguments. We introduce a leave-one-out modification of neighborhood smoothing for undirected simple graphs. When estimating a single entry P_ij, the neighborhood of node i is constructed from an adjacency matrix in which the jth row and column are set to zero, thereby decoupling neighborhood selection from the edges being averaged. We show that this construction restores conditional independence of the centered summands, enabling the use of classical probabilistic tools for inference. Under piecewise Lipschitz graphon assumptions and logarithmic degree growth, we derive variance-adaptive concentration inequalities based on Bousquet's inequality and establish Berry-Esseen bounds with explicit rates for the normalized estimation error. These results yield both finite-sample and asymptotic confidence intervals for individual edge probabilities. The same leave-one-out structure also supports an honest cross-validation scheme for tuning parameter selection, for which we prove an oracle inequality. The proposed estimator retains the optimal row-wise mean-squared error rates of classical neighborhood smoothing while providing valid entrywise uncertainty quantification.
February 3, 2026 at 8:43 PM
paperposterbot.bsky.social
arXiv📈🤖
Decision-Theoretic Robustness for Network Models
By Papamichalis, Ruane, Lunagomez et al
Bayesian network models (Erdos Renyi, stochastic block models, random dot product graphs, graphons) are widely used in neuroscience, epidemiology, and the social sciences, yet real networks are sparse, heterogeneous, and exhibit higher-order dependence. How stable are network-based decisions, model selection, and policy recommendations to small model misspecification? We study local decision-theoretic robustness by allowing the posterior to vary within a small Kullback-Leibler neighborhood and choosing actions that minimize worst-case posterior expected loss. Exploiting low-dimensional functionals available under exchangeability, we (i) adapt decision-theoretic robustness to exchangeable graphs via graphon limits and derive sharp small-radius expansions of robust posterior risk; under squared loss the leading inflation is controlled by the posterior variance of the loss, and for robustness indices that diverge at percolation/fragmentation thresholds we obtain a universal critical exponent describing the explosion of decision uncertainty near criticality. (ii) Develop a nonparametric minimax theory for robust model selection between sparse Erdos-Renyi and block models, showing-via robustness error exponents-that no Bayesian or frequentist method can uniformly improve upon the decision-theoretic limits over configuration models and sparse graphon classes for percolation-type functionals. (iii) Propose a practical algorithm based on entropic tilting of posterior or variational samples, and demonstrate it on functional brain connectivity and Karnataka village social networks.
January 7, 2026 at 4:53 PM
tmlr-pub.bsky.social
Graphon-Explainer: Generating Model-Level Explanations for Graph Neural Networks using Graphons

Sayan Saha, Sanghamitra Bandyopadhyay

Action editor: Sai Aparna Aketi

https://openreview.net/forum?id=yHUtuvoIQv

#graphon #graphons #graphs
December 16, 2024 at 6:06 AM
networkspapers.bsky.social
SIAM J. Math. Data Sci.: Generalization Bounds for Message Passing Networks on Mixture of Graphons
https://epubs.siam.org/doi/abs/10.1137/24M1651526?af=R
June 18, 2025 at 11:12 AM
mathap-bot.bsky.social
Andrea Bondesan, Jacopo Borsotti, Mattia Fontana: Kinetic models of opinion-driven epidemic dynamics modulated by graphons https://arxiv.org/abs/2604.10614 https://arxiv.org/pdf/2604.10614 https://arxiv.org/html/2604.10614
April 14, 2026 at 6:46 AM
cranberriesfeed.bsky.social
New CRAN package graphonmix with initial version 0.0.1.0
#rstats
https://cran.r-project.org/package=graphonmix
CRAN: Package graphonmix
Generates (U,W) mixture graphs where U is a line graph graphon and W is a dense graphon. Graphons are graph limits and graphon U can be written as sequence of positive numbers adding to 1. Graphs are sampled from U and W and joined randomly to obtain the mixture graph. Given a mixture graph, U can be inferred. Kandanaarachchi and Ong (2025) &lt;<a href="https://doi.org/10.48550%2FarXiv.2505.13864" target="_top">doi:10.48550/arXiv.2505.13864</a>&gt;.
cran.r-project.org
October 9, 2025 at 8:02 AM
arxiv-math-ds.bsky.social
Bisna Mary Eldo, Sarbendu Rakshit, Naoki Masuda
Dimensional reduction of dynamical systems on graphons
https://arxiv.org/abs/2503.17268
March 24, 2025 at 4:13 AM
arxiv-math-ds.bsky.social
Jason Bramburger, Matt Holzer
Capturing the critical coupling of large random Kuramoto networks with graphons
https://arxiv.org/abs/2503.01589
March 4, 2025 at 5:50 AM
samuelvaiter.com
Latent position models encompass popular random models of graphs such as SBM, Erdos-Renyi, etc. They are based on a latent space and a connectivity kernel, and strongly linked to graphons in the dense case. https://lovasz.web.elte.hu//bookxx/hombook-almost.final.pdf
February 19, 2025 at 6:00 AM