Add to ORKGAbstract. In this paper we study Ollivier’s coarse Ricci-curvature for graphs, and obtain exact formulas for the Ricci-curvature for bipartite graphs and for the graphs with girth at least 5. These are the first formulas for Ricci-curvature which hold for a wide class of graphs. We also obtain a general lower bound on the Ricci-curvature involving the size of the maximum matching in an appropriate subgraph. As a consequence, we characterize Ricci-flat graphs of girth 5, and give the first necessary and sufficient condition for the structure of Ricci-flat regular graphs of girth 4. Finally, we obtain the asymptotic Ricci-curvature of random bipartite graphs G(n, n, p) and random graphs G(n, p), in various regimes of p. 1
Connections between continuous and discrete worlds tend to be elusive. One example is curvature. Eve...
Connections between continuous and discrete worlds tend to be elusive. One example is curvature. Eve...
International audienceThe problem of defining correctly geometric objects such as the curvature is a...
Ricci curvature was proposed by Ollivier in a general framework of metric measure spaces, and it has...
Ricci curvature was proposed by Ollivier in a general framework of metric measure spaces, and it has...
We modify the definition of Ricci curvature of Ollivier of Markov chains on graphs to study the prop...
Curvature is a fundamental geometric characteristic of smooth spaces. In recent years different noti...
Curvature is a fundamental geometric characteristic of smooth spaces. In recent years different noti...
In this paper, we compare Ollivier Ricci curvature and Bakry-\'Emery curvature notions on combinator...
We classify all connected, simple, 3-regular graphs with girth at least 5 that are Ricci-flat. We us...
We classify all connected, simple, 3-regular graphs with girth at least 5 that are Ricci-flat. We us...
We classify all connected, simple, 3-regular graphs with girth at least 5 that are Ricci-flat. We us...
In this paper, we compare Ollivier Ricci curvature and Bakry-\'Emery curvature notions on combinator...
The problem of correctly defining geometric objects, such as the curvature, is a hard one in discret...
Connections between continuous and discrete worlds tend to be elusive. One example is curvature. Eve...
Connections between continuous and discrete worlds tend to be elusive. One example is curvature. Eve...
Connections between continuous and discrete worlds tend to be elusive. One example is curvature. Eve...
International audienceThe problem of defining correctly geometric objects such as the curvature is a...
Ricci curvature was proposed by Ollivier in a general framework of metric measure spaces, and it has...
Ricci curvature was proposed by Ollivier in a general framework of metric measure spaces, and it has...
We modify the definition of Ricci curvature of Ollivier of Markov chains on graphs to study the prop...
Curvature is a fundamental geometric characteristic of smooth spaces. In recent years different noti...
Curvature is a fundamental geometric characteristic of smooth spaces. In recent years different noti...
In this paper, we compare Ollivier Ricci curvature and Bakry-\'Emery curvature notions on combinator...
We classify all connected, simple, 3-regular graphs with girth at least 5 that are Ricci-flat. We us...
We classify all connected, simple, 3-regular graphs with girth at least 5 that are Ricci-flat. We us...
We classify all connected, simple, 3-regular graphs with girth at least 5 that are Ricci-flat. We us...
In this paper, we compare Ollivier Ricci curvature and Bakry-\'Emery curvature notions on combinator...
The problem of correctly defining geometric objects, such as the curvature, is a hard one in discret...
Connections between continuous and discrete worlds tend to be elusive. One example is curvature. Eve...
Connections between continuous and discrete worlds tend to be elusive. One example is curvature. Eve...
Connections between continuous and discrete worlds tend to be elusive. One example is curvature. Eve...
International audienceThe problem of defining correctly geometric objects such as the curvature is a...