The weighted Forman and Lin-Lu-Yau Ricci flow on graphs

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Bibliographic Details
Main Authors:	Bai, Shuliang, Liu, Shuang, Lai, Xin
Format:	Preprint
Published:	2026
Subjects:	Differential Geometry
Online Access:	Acceder al recurso
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author	Bai, Shuliang Liu, Shuang Lai, Xin
author_facet	Bai, Shuliang Liu, Shuang Lai, Xin
contents	In this paper, we propose a type of Ricci flow on graphs where the probability distribution for the Lin-Lu-Yau curvature remains constant over time, and also study the related Forman curvature flow. These two curvature flows coincide on trees. We first prove the existence and uniqueness of solutions for both curvature flows in general graphs. Then, we obtain that the normalized curvature flow on trees converges to a constant curvature metric, and under the uniform measure, a complete classification of trees can be obtained based on the convergence results.
format	Preprint
id	arxiv_https___arxiv_org_abs_2601_02673
institution	arXiv
publishDate	2026
record_format	arxiv
spellingShingle	The weighted Forman and Lin-Lu-Yau Ricci flow on graphs Bai, Shuliang Liu, Shuang Lai, Xin Differential Geometry In this paper, we propose a type of Ricci flow on graphs where the probability distribution for the Lin-Lu-Yau curvature remains constant over time, and also study the related Forman curvature flow. These two curvature flows coincide on trees. We first prove the existence and uniqueness of solutions for both curvature flows in general graphs. Then, we obtain that the normalized curvature flow on trees converges to a constant curvature metric, and under the uniform measure, a complete classification of trees can be obtained based on the convergence results.
title	The weighted Forman and Lin-Lu-Yau Ricci flow on graphs
topic	Differential Geometry
url	https://arxiv.org/abs/2601.02673

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