A Ricci flow on graphs from effective resistance
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arXiv
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909125925928960 |
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| 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 |