3 citations · 11 across the 11 of their papers we have counts for
11 papers
Ollivier Ricci curvature on graphs obtained by removing edges from complete graphs
Yui Asai, Taiki Yamada
Under what conditions does the sign of the Ollivier Ricci curvature on a graph of a certain order change? In this paper, we discuss the curvature of graphs obtained by removing edg…
Network analysis using Forman curvature and Shapley values on hypergraphs
Taiki Yamada
In recent years, network models have become more complex with the development of big data. Therefore, more advanced network analysis is required. In this paper, we introduce a new…
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…
The Ricci curvature on simplicial complexes
Taiki Yamada
We define the Ricci curvature on simplicial complexes by modifying the definition of the Ricci curvature on graphs, and we prove the upper and lower bounds of the Ricci curvature.…
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…
Relation between combinatorial Ricci curvature and Lin-Lu-Yau's Ricci Curvature on cell complexes
Kazuyoshi Watanabe, Taiki Yamada
In this paper we compare the combinatorial Ricci curvature on cell complexes and the LLY-Ricci curvature defined on graphs. A cell complex is correspondence to a graph such that th…
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…
The Ricci curvature on directed graphs
Taiki Yamada
In this paper, we consider the Ricci curvature of a directed graph, based on Lin-Lu-Yau's definition. We give some properties of the Ricci curvature, including conditions for a dir…