A Ricci flow on graphs from effective resistance

Fuente: arXiv
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Main Authors: Dawkins, Aleyah, Gupta, Vishal, Kempton, Mark, Linz, William, Quail, Jeremy, Richman, Harry, Stier, Zachary
Format: Preprint
Published: 2024
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_version_ 1866909125925928960
author Dawkins, Aleyah
Gupta, Vishal
Kempton, Mark
Linz, William
Quail, Jeremy
Richman, Harry
Stier, Zachary
author_facet Dawkins, Aleyah
Gupta, Vishal
Kempton, Mark
Linz, William
Quail, Jeremy
Richman, Harry
Stier, Zachary
contents In this paper, we introduce a new notion of curvature on the edges of a graph that is defined in terms of effective resistances. We call this the Ricci--Foster curvature. We study the Ricci flow resulting from this curvature. We prove the existence of solutions to Ricci flow on short time intervals, and prove that Ricci flow preserves graphs with nonnegative (resp. positive) curvature.
format Preprint
id arxiv_https___arxiv_org_abs_2403_01151
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle A Ricci flow on graphs from effective resistance
Dawkins, Aleyah
Gupta, Vishal
Kempton, Mark
Linz, William
Quail, Jeremy
Richman, Harry
Stier, Zachary
Combinatorics
Differential Geometry
05C10, 53E20, 05C22, 53A70, 53C21, 94C15
In this paper, we introduce a new notion of curvature on the edges of a graph that is defined in terms of effective resistances. We call this the Ricci--Foster curvature. We study the Ricci flow resulting from this curvature. We prove the existence of solutions to Ricci flow on short time intervals, and prove that Ricci flow preserves graphs with nonnegative (resp. positive) curvature.
title A Ricci flow on graphs from effective resistance
topic Combinatorics
Differential Geometry
05C10, 53E20, 05C22, 53A70, 53C21, 94C15
url https://arxiv.org/abs/2403.01151