{"ID":2850622,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.21392","arxiv_id":"2510.21392","title":"On Local Limits of Sparse Random Graphs: Color Convergence and the Refined Configuration Model","abstract":"Local convergence has emerged as a fundamental tool for analyzing sparse random graph models. We introduce a new notion of local convergence, color convergence, based on the Weisfeiler-Leman algorithm. Color convergence fully characterizes the class of random graphs that are well-behaved in the limit for message-passing graph neural networks. Building on this, we propose the Refined Configuration Model (RCM), a random graph model that generalizes the configuration model. The RCM is universal with respect to local convergence among locally tree-like random graph models, including Erdős-Rényi, stochastic block and configuration models. Finally, this framework enables a complete characterization of the random trees that arise as local limits of such graphs.","short_abstract":"Local convergence has emerged as a fundamental tool for analyzing sparse random graph models. We introduce a new notion of local convergence, color convergence, based on the Weisfeiler-Leman algorithm. Color convergence fully characterizes the class of random graphs that are well-behaved in the limit for message-passin...","url_abs":"https://arxiv.org/abs/2510.21392","url_pdf":"https://arxiv.org/pdf/2510.21392v1","authors":"[\"Alexander Pluska\",\"Sagar Malhotra\"]","published":"2025-10-24T12:29:51Z","proceeding":"cs.DM","tasks":"[\"cs.DM\",\"cs.LG\"]","methods":"[\"Graph Neural Network\"]","has_code":false}