We define a hybrid between Ollivier and Bakry-Emery curvature on graphs with dependence on a variable neighborhood. The hexagonal lattice is non-negatively curved under this new curvature notion. Bonnet-Myers diameter bounds and Lichnerowicz eigenvalue estimates follow from the standard arguments. We prove gradient estimates similar to the ones obtained from Bakry-Emery curvature allowing us to prove Harnack and Buser inequalities.

中文翻译：

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图上的大Ricci曲率

我们在图上定义了Ollivier和Bakry-Emery曲率之间的混合，并依赖于可变邻域。在这个新的曲率概念下，六角形晶格非负弯曲。Bonnet-Myers直径范围和Lichnerowicz特征值估计值均来自标准参数。我们证明了梯度估计与从Bakry-Emery曲率获得的近似，从而证明了Harnack和Buser不等式。