On the relation between graph Ricci curvature and community structure
The connection between curvature and topology is a very well-studied theme in the subject of differential geometry. By suitably defining curvature on networks, the study of this theme has been extended into the domain of network analysis as well. In particular, this has led to curvature-based commun...
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| Format: | Article |
| Language: | English |
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AIMS Press
2025-04-01
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| Series: | Mathematics in Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mine.2025008 |
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| _version_ | 1850254609569808384 |
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| author | Sathya Rengaswami Theodora Bourni Vasileios Maroulas |
| author_facet | Sathya Rengaswami Theodora Bourni Vasileios Maroulas |
| author_sort | Sathya Rengaswami |
| collection | DOAJ |
| description | The connection between curvature and topology is a very well-studied theme in the subject of differential geometry. By suitably defining curvature on networks, the study of this theme has been extended into the domain of network analysis as well. In particular, this has led to curvature-based community detection algorithms. In this paper, we reveal the relation between community structure of a network and the curvature of its edges. In particular, we give apriori bounds on the curvature of intercommunity edges of a graph. |
| format | Article |
| id | doaj-art-201e7df2e77b47d885603522da742885 |
| institution | OA Journals |
| issn | 2640-3501 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematics in Engineering |
| spelling | doaj-art-201e7df2e77b47d885603522da7428852025-08-20T01:57:05ZengAIMS PressMathematics in Engineering2640-35012025-04-017217819310.3934/mine.2025008On the relation between graph Ricci curvature and community structureSathya Rengaswami0Theodora Bourni1Vasileios Maroulas2Department of Mathematics, University of Tennessee, Knoxville TN 37916, USADepartment of Mathematics, University of Tennessee, Knoxville TN 37916, USADepartment of Mathematics, University of Tennessee, Knoxville TN 37916, USAThe connection between curvature and topology is a very well-studied theme in the subject of differential geometry. By suitably defining curvature on networks, the study of this theme has been extended into the domain of network analysis as well. In particular, this has led to curvature-based community detection algorithms. In this paper, we reveal the relation between community structure of a network and the curvature of its edges. In particular, we give apriori bounds on the curvature of intercommunity edges of a graph.https://www.aimspress.com/article/doi/10.3934/mine.2025008discrete curvatureollivier ricci curvaturegraph curvatureoptimal transportcommunity structurecommunity detection |
| spellingShingle | Sathya Rengaswami Theodora Bourni Vasileios Maroulas On the relation between graph Ricci curvature and community structure Mathematics in Engineering discrete curvature ollivier ricci curvature graph curvature optimal transport community structure community detection |
| title | On the relation between graph Ricci curvature and community structure |
| title_full | On the relation between graph Ricci curvature and community structure |
| title_fullStr | On the relation between graph Ricci curvature and community structure |
| title_full_unstemmed | On the relation between graph Ricci curvature and community structure |
| title_short | On the relation between graph Ricci curvature and community structure |
| title_sort | on the relation between graph ricci curvature and community structure |
| topic | discrete curvature ollivier ricci curvature graph curvature optimal transport community structure community detection |
| url | https://www.aimspress.com/article/doi/10.3934/mine.2025008 |
| work_keys_str_mv | AT sathyarengaswami ontherelationbetweengraphriccicurvatureandcommunitystructure AT theodorabourni ontherelationbetweengraphriccicurvatureandcommunitystructure AT vasileiosmaroulas ontherelationbetweengraphriccicurvatureandcommunitystructure |