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

Ryunosuke Ozawa; Yohei Sakurai; Taiki Yamada

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

Ryunosuke Ozawa, Yohei Sakurai, Taiki Yamada

Advanced Institute for Materials Research (AIMR)

Research output: Contribution to journal › Article › peer-review

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.

MSC Codes 05C20, 05C12, 05C81, 53C21, 53C23

Original language	English
Journal	Unknown Journal
Publication status	Published - 2019 Sep 17

Keywords

Comparison geometry
Directed graph
Eigenvalue of Laplacian
Ricci curvature

ASJC Scopus subject areas

General

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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.MSC Codes 05C20, 05C12, 05C81, 53C21, 53C23",

keywords = "Comparison geometry, Directed graph, Eigenvalue of Laplacian, Ricci curvature",

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T1 - Geometric and spectral properties of directed graphs under a lower ricci curvature bound

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AU - Sakurai, Yohei

AU - Yamada, Taiki

PY - 2019/9/17

Y1 - 2019/9/17

N2 - 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.MSC Codes 05C20, 05C12, 05C81, 53C21, 53C23

AB - 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.MSC Codes 05C20, 05C12, 05C81, 53C21, 53C23

KW - Comparison geometry

KW - Directed graph

KW - Eigenvalue of Laplacian

KW - Ricci curvature

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