{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/the-graph-curvature-calculator-and-the","title":"The Graph Curvature Calculator and the curvatures of cubic graphs","arxiv_id":"1712.03033","date":"2017-12-08","proceeding":null,"authors":["David Cushing","Riikka Kangaslampi","Valtteri Lipiäinen","Shiping Liu","George William Stagg"],"abstract":"We classify all cubic graphs with either non-negative Ollivier-Ricci curvature or non-negative Bakry-\\'Emery curvature everywhere. We show in both curvature notions that the non-negatively curved graphs are the prism graphs and the M\\\"obius ladders. We also highlight an online tool for calculating the curvature of graphs under several variants of these curvature notions that we use in the classification. As a consequence of the classification result we show, that non-negatively curved cubic expanders do not exist.","url_abs":"http://arxiv.org/abs/1712.03033v2","url_pdf":"http://arxiv.org/pdf/1712.03033v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"the-graph-curvature-calculator-and-the","repo_url":"https://github.com/spakula/graph-curvature-python","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}