3 citations · 11 across the 11 of their papers we have counts for
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Heat flow and concentration of measure on directed graphs with a lower Ricci curvature bound
Ryunosuke Ozawa, Yohei Sakurai, Taiki Yamada
In a previous work, the authors introduced a Lin-Lu-Yau type Ricci curvature for directed graphs referring to the formulation of the Chung Laplacian. The aim of this note is to pro…
Maximal diameter theorem for directed graphs of positive Ricci curvature
Ryunosuke Ozawa, Yohei Sakurai, Taiki Yamada
In a previous work, the authors have introduced a Lin-Lu-Yau type Ricci curvature for directed graphs, and obtained a diameter comparison of Bonnet-Myers type. In this paper, we in…
Geometric and spectral properties of directed graphs under a lower Ricci curvature bound
Ryunosuke Ozawa, Yohei Sakurai, Taiki Yamada
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 discu…
A construction of graphs with positive Ricci curvature
Taiki Yamada
Two complete graphs are connected by adding some edges. The obtained graph is called the gluing graph. The more we add edges, the larger the Ricci curvature on it becomes. We calcu…
An estimate of the first non-zero eigenvalue of the Laplacian by the Ricci curvature on edges of graphs
Taiki Yamada
We define the distance between edges of graphs and study the coarse Ricci curvature on edges. We consider the Laplacian on edges based on the Jost-Horak's definition of the Laplaci…
Curvature dimension inequalities on directed graphs
Taiki Yamada
In this paper, we define the curvature dimension inequalities CD(m, K) on finite directed graphs modifying the case of undirected graphs. As a main result, we evaluate m and K on f…