A Ricci flow on graphs from effective resistance

A Ricci flow on graphs from effective resistance

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,...

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Veröffentlicht in:arXiv.org 2024-03
Hauptverfasser: Dawkins, Aleyah, Gupta, Vishal, Kempton, Mark, Linz, William, Quail, Jeremy, Richman, Harry, Stier, Zachary
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Curvature
Graph theory
Graphs
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Gupta, Vishal
Kempton, Mark
Linz, William
Quail, Jeremy
Richman, Harry
Stier, Zachary
description 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.
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Graphs
title A Ricci flow on graphs from effective resistance
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