Geometric and spectral properties of directed graphs under a lower Ricci curvature bound
Geometric and spectral properties of directed graphs under a lower Ricci curvature bound
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DOI：
10.1007/s00526-020-01809-2
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发表时间：
2019-09
影响因子：
2.1
通讯作者：
Ryunosuke Ozawa;Y. Sakurai;Taiki Yamada
中科院分区：
文献类型：
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作者：
Ryunosuke Ozawa;Y. Sakurai;Taiki Yamada
对于无向图，Lin-Lu-Yau引入的Ricci曲率已经从各种角度，特别是几何分析的角度得到了广泛的研究。本文讨论了有向图的Ricci曲率的推广问题。我们引入了一个新的推广强连通有向图使用的平均转移概率核出现在制定的Chung拉普拉斯算子。在Ricci曲率下界下，我们得到了一些几何和谱性质，推广了无向情形下的已有结果。
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.