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

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 m...

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Bibliographic Details
Published in:arXiv.org 2020-07
Main Authors: Ozawa, Ryunosuke, Sakurai, Yohei, Yamada, Taiki
Format: Article
Language:English
Subjects:
Curvature
Graph theory
Graphs
Logic programming
Transition probabilities
Online Access:Get full text
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Summary: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.
ISSN:2331-8422