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math.DG2017★ 2 cited
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…
math.DG2017★ 3 cited
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…