16 citations · 17 across the 14 of their papers we have counts for
18 papers
A generalized Cheeger inequality and the Steklov Problem on finite graphs
Bobo Hua, Supanat Kamtue, Shiping Liu +2
We prove generalized Cheeger inequalities for eigenvalues of Laplacians for reversible Markov chains. Then we apply Hassannezhad and Miclo's convergence result to obtain Jammes Che…
On a magneto-spectral invariant on finite graphs
Chunyang Hu, Bobo Hua, Supanat Kamtue +3
In this paper, we introduce a magneto-spectral invariant for finite graphs. This invariant vanishes on trees and is maximized by complete graphs. We compute this invariant for cycl…
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…
Entropic curvature not comparable to other curvatures -- or is it?
Supanat Kamtue, Shiping Liu, Florentin Münch +1
In this paper we consider global -curvatures of finite Markov chains with associated means in the spirit of the entropic curvature (based on the logarithmic mean) by Erbar-M…
Bakry-Émery calculus for entropic curvature, new diameter estimates, and spectral gaps
Supanat Kamtue, Shiping Liu, Florentin Münch +1
In this paper, we propose a generalization of Bakry-Émery's calculus which allows us to formulate both Bakry-Émery and entropic curvature simultaneously. This formulation represent…
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…
Bakry-Émery curvature sharpness and curvature flow in finite weighted graphs. II. Implementation
David Cushing, Supanat Kamtue, Shiping Liu +3
In this second part of a sequence of two papers, we discuss the implementation of a curvature flow on weighted graphs based on the Bakry-Émery calculus. This flow can be adapted to…
Bakry-Émery curvature sharpness and curvature flow in finite weighted graphs. I. Theory
David Cushing, Supanat Kamtue, Shiping Liu +3
In this sequence of two papers, we introduce a curvature flow on (mixed) weighted graphs which is based on the Bakry-Émery calculus. The flow is described via a time-continuous evo…
Disentangling global equity market instability: a network analysis
Supanat Kamtue, Pongsak Luangaram, Sirawit Woramongkhon
During a financial crisis, the capital markets network frequently exhibits a high correlation between returns. We developed a network analysis framework based on daily returns from…
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…
A note on a Bonnet-Myers type diameter bound for graphs with positive entropic Ricci curvature
Supanat Kamtue
An equivalent definition of entropic Ricci curvature on discrete spaces was given in terms of the global gradient estimate. With a particular choice of the density function , we…
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…