图的长尺度Ollivier Ricci曲率

Pub Date : 2018-01-30 DOI:10.1515/agms-2019-0003

D. Cushing, S. Kamtue

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引用次数: 8

摘要

研究了图的长尺度奥利维耶·里奇曲率作为所选空闲量的函数。与之前在短尺度情况下的工作类似，我们证明了该空闲函数是凹的，分段线性的，最多有3个线性部分。我们给出了第一个和最后一个线性片段的长度界限。我们还研究了两个正则图的笛卡尔积的长尺度曲率。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Long-Scale Ollivier Ricci Curvature of Graphs

Abstract We study the long-scale Ollivier Ricci curvature of graphs as a function of the chosen idleness. Similarly to the previous work on the short-scale case, we show that this idleness function is concave and piecewise linear with at most 3 linear parts. We provide bounds on the length of the first and last linear pieces. We also study the long-scale curvature for the Cartesian product of two regular graphs.

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