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The Graph Curvature Calculator and the curvatures of cubic graphs

Research output: Contribution to journalArticleScientificpeer-review

Details

Original languageEnglish
JournalExperimental Mathematics
Early online date14 Sep 2019
DOIs
Publication statusE-pub ahead of print - 14 Sep 2019
Publication typeA1 Journal article-refereed

Abstract

We classify all cubic graphs with either non-negative Ollivier-Ricci curvature or non-negative Bakry-Émery curvature everywhere. We show in both curvature notions that the non-negatively curved graphs are the prism graphs and the Möbius 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.

Publication forum classification

Field of science, Statistics Finland