Coarse Ricci curvature of hypergraphs and its generalization
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
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| _version_ | 1866917207931355136 |
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| author | Ikeda, MasaHiro Kitabeppu, Yu Takai, Yuuki Uehara, Takato |
| author_facet | Ikeda, MasaHiro Kitabeppu, Yu Takai, Yuuki Uehara, Takato |
| contents | In the present paper, we introduce a concept of Ricci curvature on hypergraphs for a nonlinear Laplacian. We prove that our definition of the Ricci curvature is a generalization of Lin-Lu-Yau coarse Ricci curvature for graphs to hypergraphs. We also show a lower bound of nonzero eigenvalues of Laplacian, gradient estimate of heat flow, and diameter bound of Bonnet-Myers type for our curvature notion. This research leads to understanding how nonlinearity of Laplacian causes complexity of curvatures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2102_00698 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Coarse Ricci curvature of hypergraphs and its generalization Ikeda, MasaHiro Kitabeppu, Yu Takai, Yuuki Uehara, Takato Metric Geometry In the present paper, we introduce a concept of Ricci curvature on hypergraphs for a nonlinear Laplacian. We prove that our definition of the Ricci curvature is a generalization of Lin-Lu-Yau coarse Ricci curvature for graphs to hypergraphs. We also show a lower bound of nonzero eigenvalues of Laplacian, gradient estimate of heat flow, and diameter bound of Bonnet-Myers type for our curvature notion. This research leads to understanding how nonlinearity of Laplacian causes complexity of curvatures. |
| title | Coarse Ricci curvature of hypergraphs and its generalization |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2102.00698 |