Ollivier Ricci curvature on graphs obtained by removing edges from complete graphs
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910271643058176 |
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| author | Asai, Yui Yamada, Taiki |
| author_facet | Asai, Yui Yamada, Taiki |
| contents | Under what conditions does the sign of the Ollivier Ricci curvature on a graph of a certain order change? In this paper, we discuss the curvature of graphs obtained by removing edges from complete graphs, as complete graphs have a stable positive curvature. We defined graphs obtained by removing matching edges, the set of edges incident with the vertex, and cycle edges from complete graphs, and then analyzed the Ollivier Ricci curvature of those graphs. The results show that the curvature of the graphs in the above three patterns is equal to the value obtained by dividing the number of triangles, including two vertices, by the maximum degree of the two vertices. This result also indicates that the curvature of the above graphs is zero or positive. This study concludes that the Ollivier Ricci curvature is predicted to be positive even if some edges are removed from a complete graph, and we suggest that these discussions are suitable for investigating the conditions under which the sign of the Ollivier Ricci curvature on a graph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_30830 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Ollivier Ricci curvature on graphs obtained by removing edges from complete graphs Asai, Yui Yamada, Taiki Combinatorics Differential Geometry 05C12, 52C99 Under what conditions does the sign of the Ollivier Ricci curvature on a graph of a certain order change? In this paper, we discuss the curvature of graphs obtained by removing edges from complete graphs, as complete graphs have a stable positive curvature. We defined graphs obtained by removing matching edges, the set of edges incident with the vertex, and cycle edges from complete graphs, and then analyzed the Ollivier Ricci curvature of those graphs. The results show that the curvature of the graphs in the above three patterns is equal to the value obtained by dividing the number of triangles, including two vertices, by the maximum degree of the two vertices. This result also indicates that the curvature of the above graphs is zero or positive. This study concludes that the Ollivier Ricci curvature is predicted to be positive even if some edges are removed from a complete graph, and we suggest that these discussions are suitable for investigating the conditions under which the sign of the Ollivier Ricci curvature on a graph. |
| title | Ollivier Ricci curvature on graphs obtained by removing edges from complete graphs |
| topic | Combinatorics Differential Geometry 05C12, 52C99 |
| url | https://arxiv.org/abs/2605.30830 |