16 citations · 17 across the 14 of their papers we have counts for
10 papers · 1 filter
A note on Steinerberger's curvature for graphs
David Cushing, Supanat Kamtue, Erin Law +3
In this note, we provide Steinerberger curvature formulas for block graphs, discuss curvature relations between two graphs and the graph obtained by connecting them via a bridge, a…
Bakry-Émery and Ollivier Ricci Curvature of Cayley Graphs
David Cushing, Supanat Kamtue, Riikka Kangaslampi +3
In this article we study two discrete curvature notions, Bakry-Émery curvature and Ollivier Ricci curvature, on Cayley graphs. We introduce Right Angled Artin-Coxeter Hybrids (RAAC…
Transportation Distance between Probability Measures on the Infinite Regular Tree
Pakawut Jiradilok, Supanat Kamtue
In the infinite regular tree with , we consider families , indexed by vertices and nonnegative integers ("discrete time…
Bakry-Émery curvature on graphs as an eigenvalue problem
David Cushing, Supanat Kamtue, Shiping Liu +1
In this paper, we reformulate the Bakry-Émery curvature on a weighted graph in terms of the smallest eigenvalue of a rank one perturbation of the so-called curvature matrix using S…
Bonnet-Myers sharp graphs of diameter three
Supanat Kamtue
Regular graphs which are Bonnet-Myers sharp (in the sense of Ollivier Ricci curvature) and self-centered have been completely classified, and it is a natural question whether the c…
Curvatures, graph products and Ricci flatness
David Cushing, Supanat Kamtue, Riikka Kangaslampi +2
In this paper, we compare Ollivier Ricci curvature and Bakry-Émery curvature notions on combinatorial graphs and discuss connections to various types of Ricci flatness. We show tha…
Quartic graphs which are Bakry-Émery curvature sharp
David Cushing, Supanat Kamtue, Norbert Peyerimhoff +1
We give a classification of all connected quartic graphs which are (infinity) curvature sharp in all vertices with respect to Bakry-Émery curvature. The result is based on a comput…
Rigidity of the Bonnet-Myers inequality for graphs with respect to Ollivier Ricci curvature
David Cushing, Supanat Kamtue, Jack Koolen +3
We introduce the notion of Bonnet-Myers and Lichnerowicz sharpness in the Ollivier Ricci curvature sense. Our main result is a classification of all self-centered Bonnet-Myers shar…
Combinatorial, Bakry-Émery, Ollivier's Ricci curvature notions and their motivation from Riemannian geometry
Supanat Kamtue
In this survey, we study three different notions of curvature that are defined on graphs, namely, combinatorial curvature, Bakry-Émery curvature, and Ollivier's Ricci curvature. Fo…
Long scale Ollivier-Ricci curvature of graphs
David Cushing, Supanat Kamtue
We study the long scale Ollivier-Ricci curvature of graphs as a function of the chosen idleness. As in the previous work on the short scale, we show that this idleness function is…