For undirected graphs, the Ricci curvature introduced by Lin-Lu-Yau has been widely studied from various perspectives, especially geometric analysis. In the present paper, we discuss generalization problem of their Ricci curvature for directed graphs. We introduce a new generalization for strongly connected directed graphs by using the mean transition probability kernel which appears in the formulation of the Chung Laplacian. We conclude several geometric and spectral properties under a lower Ricci curvature bound extending previous results in the undirected case.

中文翻译：

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Ricci曲率下界下有向图的几何和光谱性质

对于无向图，Lin-Lu-Yau引入的Ricci曲率已从各种角度进行了广泛研究，尤其是几何分析。在本文中，我们讨论了有向图的Ricci曲率的推广问题。通过使用在Chung Laplacian公式中出现的平均跃迁概率核，我们为强连通有向图引入了一种新的概括。我们在较低的Ricci曲率边界下得出了几种几何和光谱特性的结论，扩展了无向情况下的先前结果。