The Graph Curvature Calculator and the Curvatures of Cubic Graphs
The Graph Curvature Calculator and the Curvatures of Cubic Graphs
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DOI：
10.1080/10586458.2019.1660740
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发表时间：
2017-12
影响因子：
0.5
通讯作者：
D. Cushing;Riikka Kangaslampi;Valtteri Lipiäinen;Shiping Liu;G. Stagg
中科院分区：
文献类型：
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作者：
D. Cushing;Riikka Kangaslampi;Valtteri Lipiäinen;Shiping Liu;G. Stagg
摘要我们对处处具有非负Ollivier-Ricci曲率或非负Bakry-Émery曲率的三次图进行了分类。在这两个曲率概念中，我们证明了非负曲线图是棱柱图和Möbius阶图。分类结果表明，非负曲线立方膨胀机是不存在的。我们还介绍了图曲率计算器，这是一个在线工具，用于在分类中使用的曲率概念的几个变体下计算图的曲率。
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. As a consequence of the classification result we show that non-negatively curved cubic expanders do not exist. We also introduce the Graph Curvature Calculator, an online tool developed for calculating the curvature of graphs under several variants of the curvature notions that we use in the classification.