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arXiv · 1909.07715

Geometric and spectral properties of directed graphs under a lower Ricci curvature bound

Ryunosuke Ozawa·Yohei Sakurai·Taiki Yamada
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Abstract

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 by using the mean transition probability kernel which appears in the formulation of the Chung Laplacian. We conclude several geometric and spectral properties of directed graphs under a lower Ricci curvature bound extending previous results in the undirected case.

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Ryunosuke Ozawa, Yohei Sakurai, Taiki Yamada. 2019-09-17. Geometric and spectral properties of directed graphs under a lower Ricci curvature bound. https://arxiv.org/abs/1909.07715

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