A Ricci flow on graphs from effective resistance
Combinatorics
2024-03-05 v1 Differential Geometry
Abstract
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.
Cite
@article{arxiv.2403.01151,
title = {A Ricci flow on graphs from effective resistance},
author = {Aleyah Dawkins and Vishal Gupta and Mark Kempton and William Linz and Jeremy Quail and Harry Richman and Zachary Stier},
journal= {arXiv preprint arXiv:2403.01151},
year = {2024}
}
Comments
14 pages, 8 figures, comments welcome!