#graphon
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mathpr-bot.bsky.social
Robert Lunde, Soumendra Lahiri: Uniform Central Limit Theorems for Degree Distributions of Sparse Graphon Models https://arxiv.org/abs/2611.06892 https://arxiv.org/pdf/2611.06892 https://arxiv.org/html/2611.06892
November 5, 2026 at 6:50 AM
aoihal-ppbot.bsky.social
Abu Safyan Ali, Elisa Calzola, Giacomo Dimarco, Lorenzo Pareschi, Thomas Rey: How opinions shape epidemics: a graphon-based kinetic approach https://hal.science/hal-05842353v1 [math]
October 30, 2026 at 3:00 AM
mathco-bot.bsky.social
Svante Janson, Tiffany Y. Y. Lo, Colin McDiarmid, Anda Skeja, Fiona Skerman: Graphon Colourings and Limits of Graph Partitions https://arxiv.org/abs/2610.38599 https://arxiv.org/pdf/2610.38599 https://arxiv.org/html/2610.38599
October 30, 2026 at 6:47 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
shubhendu.bsky.social
But for each of the "pivot switches" above (in order), some references are (not an expert by any means either, but also learning). (1) Carmona & Delarue (2018), Probabilistic Theory of Mean Field Games with Applications (Volumes I & II) and Parise & Ozdaglar (2023), Graphon Games; (2)
October 26, 2026 at 10:12 PM
arxivecongnbot.bsky.social
arXiv📈🤖
Hybrid of node and link communities for graphon estimation
By
Networks serve as a tool used to examine the large-scale connectivity patterns in complex systems. Modelling their generative mechanism nonparametrically is often based on step-functions, such as the stochastic block models. These models are capable of addressing two prominent topics in network science: link prediction and community detection. However, such methods often have a resolution limit, making it difficult to separate small-scale structures from noise. To arrive at a smoother representation of the network's generative mechanism, we explicitly trade variance for bias by smoothing blocks of edges based on stochastic equivalence. As such, we propose a different estimation method using a new model, which we call the stochastic shape model. Typically, analysis methods are based on modelling node or link communities. In contrast, we take a hybrid approach, bridging the two notions of community. Consequently, we obtain a more parsimonious representation, enabling a more interpretable and multiscale summary of the network structure. By considering multiple resolutions, we trade bias and variance to ensure that our estimator is rate-optimal. We also examine the performance of our model through simulations and applications to real network data.
October 29, 2026 at 8:53 PM
optb0t.bsky.social
📚 New Arxiv Paper

Title: Optimal Graphon Control of Collective Dynamics
Authors: Joseph K. Miller, Brandon Su

Read more: https://arxiv.org/abs/2610.31975
October 26, 2026 at 8:02 AM
mathoc-bot.bsky.social
Joseph K. Miller, Brandon Su: Optimal Graphon Control of Collective Dynamics https://arxiv.org/abs/2610.31975 https://arxiv.org/pdf/2610.31975 https://arxiv.org/html/2610.31975
October 26, 2026 at 6:49 AM
mathst-bot.bsky.social
Justin R. Baars, Roger J. A. Laeven, Michel R. H. Mandjes: Graphon Hawkes Processes: Sparse Estimation and Network Recovery https://arxiv.org/abs/2610.16677 https://arxiv.org/pdf/2610.16677 https://arxiv.org/html/2610.16677
October 14, 2026 at 6:51 AM
arxiv-cs-si.bsky.social
Explicit Bounds on the Entropy of Piecewise H\"{o}lder Graphon Models
https://arxiv.org/abs/2608.26501
October 9, 2026 at 3:34 PM
llmrelevance.bsky.social
New tool added to our directory: Graphon AI
New tool: Graphon AI
Graphon AI is a multimodal memory tool that connects significant moments, entities, and contexts across various media types. It enhances AI capabilities.
www.llmrelevance.com
October 5, 2026 at 11:49 AM
optb0t.bsky.social
📚 New Arxiv Paper

Title: General Leader-Follower Linear-Quadratic Stochastic Graphon Games with Indefinite Control Weights
Authors: Weijia Chen, Jingtao Shi

Read more: https://arxiv.org/abs/2609.24185
September 22, 2026 at 8:02 AM
mathoc-bot.bsky.social
Weijia Chen, Jingtao Shi: General Leader-Follower Linear-Quadratic Stochastic Graphon Games with Indefinite Control Weights https://arxiv.org/abs/2609.24185 https://arxiv.org/pdf/2609.24185 https://arxiv.org/html/2609.24185
September 22, 2026 at 6:50 AM
mathst-bot.bsky.social
Chiara Amorino, Matteo Sfragara: Parameter estimation for graphon-interacting particle systems from discrete observations https://arxiv.org/abs/2609.21710 https://arxiv.org/pdf/2609.21710 https://arxiv.org/html/2609.21710
September 21, 2026 at 6:50 AM
mathco-bot.bsky.social
Dean Menezes: A Direct Proof of the Locally Dense Graphon Inequality https://arxiv.org/abs/2609.19014 https://arxiv.org/pdf/2609.19014 https://arxiv.org/html/2609.19014
September 17, 2026 at 6:47 AM
mathpr-bot.bsky.social
Sebastian Grube, Guodong Pang, Michael R\"ockner: On Solutions to Graphon McKean-Vlasov SDEs of Nemytskii-type https://arxiv.org/abs/2609.19084 https://arxiv.org/pdf/2609.19084 https://arxiv.org/html/2609.19084
September 17, 2026 at 6:50 AM
repec-nep-net.bsky.social
Low-rank and graphon limits for dynamic threshold distress contagion in heterogeneous financial networks: Pengbin Feng
NEP/RePEc link
to paper
d.repec.org
September 9, 2026 at 11:51 PM
optb0t.bsky.social
📚 New Arxiv Paper

Title: Extended Graphon Mean-Field Games in Discrete Time
Authors: Hamed Amini, Zhongyuan Cao, G\"ok\c{c}e Dayan{\i}kl{\i}, Mathieu Lauri\`ere, Kexin Shao, Agn\`es Sulem

Read more: https://arxiv.org/abs/2609.04737
September 7, 2026 at 8:02 AM
mathoc-bot.bsky.social
Hamed Amini, Zhongyuan Cao, G\"ok\c{c}e Dayan{\i}kl{\i}, Mathieu Lauri\`ere, Kexin Shao, Agn\`es Sulem: Extended Graphon Mean-Field Games in Discrete Time https://arxiv.org/abs/2609.04737 https://arxiv.org/pdf/2609.04737 https://arxiv.org/html/2609.04737
September 7, 2026 at 6:49 AM
arxivecongnbot.bsky.social
arXiv📈🤖
Low-Rank Approaches to Graphon Learning in Networks
By Fan, Ma, Leng et al
The graphon is a powerful framework for modeling large-scale networks, but its estimation remains a significant challenge. In this paper, we propose a novel approach that directly leverages a low-rank representation of the graphon for parsimonious modeling. This representation naturally yields both a low-rank connection probability matrix and a low-rank graphon -- two tasks that are often infeasible in existing literature -- while also addressing the well-known identification issues in graphon estimation. By exploiting the additive structure of this representation, we develop an efficient sequential learning algorithm that estimates the low-rank connection matrix using subgraph counts and reconstructs the graphon function through interpolation. We establish the consistency of the proposed method and demonstrate its computational efficiency and estimation accuracy through extensive simulation studies.
September 4, 2026 at 9:15 PM
optb0t.bsky.social
🔄 Updated Arxiv Paper

Title: Convex ordering for graphon mean-field systems
Authors: Daorong Cui, Shuoqing Deng, Yang Xiang

Read more: https://arxiv.org/abs/2608.19576
September 3, 2026 at 8:02 AM
statco-bot.bsky.social
Youngseok Song, Sofia C. Olhede: nethist: An R package for Nonparametric Graphon Estimation via Network Histograms https://arxiv.org/abs/2609.01937 https://arxiv.org/pdf/2609.01937 https://arxiv.org/html/2609.01937
September 3, 2026 at 7:02 AM
cranupdates.bsky.social
New on CRAN: nethist (1.0.0). View at https://CRAN.R-project.org/package=nethist
nethist: Network Histograms
Estimates network histograms, a blockmodel approximation to the graphon underlying a network's connectivity pattern, for both single-layer and multilayer networks. Implements graphon estimation methods including the profile-likelihood method of Olhede and Wolfe (2014) &lt;<a href="https://doi.org/10.1073%2Fpnas.1400374111" target="_top">doi:10.1073/pnas.1400374111</a>&gt; and the least-squares method of Gao, Lu, and Zhou (2015) &lt;<a href="https://doi.org/10.1214%2F15-AOS1354" target="_top">doi:10.1214/15-AOS1354</a>&gt; for single-layer networks, and the multilayer extension of Song and Olhede (2026) &lt;<a href="https://doi.org/10.48550%2FarXiv.2608.14536" target="_top">doi:10.48550/arXiv.2608.14536</a>&gt;.
CRAN.R-project.org
September 2, 2026 at 1:17 PM
cranberriesfeed.bsky.social
New CRAN package nethist with initial version 1.0.0
#rstats
https://cran.r-project.org/package=nethist
CRAN: Package nethist
Estimates network histograms, a blockmodel approximation to the graphon underlying a network's connectivity pattern, for both single-layer and multilayer networks. Implements graphon estimation methods including the profile-likelihood method of Olhede and Wolfe (2014) &lt;<a href="https://doi.org/10.1073%2Fpnas.1400374111" target="_top">doi:10.1073/pnas.1400374111</a>&gt; and the least-squares method of Gao, Lu, and Zhou (2015) &lt;<a href="https://doi.org/10.1214%2F15-AOS1354" target="_top">doi:10.1214/15-AOS1354</a>&gt; for single-layer networks, and the multilayer extension of Song and Olhede (2026) &lt;<a href="https://doi.org/10.48550%2FarXiv.2608.14536" target="_top">doi:10.48550/arXiv.2608.14536</a>&gt;.
cran.r-project.org
September 2, 2026 at 12:02 PM
eesssy-bot.bsky.social
Zhewei Wang, Vu Anh Phi, Marcos M. Vasconcelos: Graphon Design for Human-Machine Coordination under Bounded Rationality: Optimality of Stochastic Block Models https://arxiv.org/abs/2608.27851 https://arxiv.org/pdf/2608.27851 https://arxiv.org/html/2608.27851
August 31, 2026 at 6:46 AM