7 papers · 1 filter
Equivalence of Lin--Lu--Yau curvature and 1/2-Ollivier curvature on weighted graphs
Shiping Liu, Yunyan Yang
In this note, we prove that, on weighted graphs, the Lin--Lu--Yau curvature coincides with the -Ollivier curvature up to scaling whenever the idleness parameter . Mor…
Regular Lichnerowicz-sharp graphs are hypercube bundles
Yanlong Ding, Shiping Liu, Chiyu Zhou
Hypercube graphs are fundamental model spaces of positive curvature in discrete comparison geometry. Let be a finite, connected, simple, unweighted graph with Bakry--Émery curv…
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…
Quantitative Obata's theorem in discrete setting
Shiping Liu, Chiyu Zhou
Under mild assumptions, we show that a connected weighted graph with lower Ricci curvature bound in the sense of Bakry-Ãmery and the -th non-zero Laplacian eigenvalue…
Ricci curvature, diameter and eigenvalues of amply regular graphs
Kaizhe Chen, Chunyang Hu, Shiping Liu +1
Amply regular graphs are graphs with local distance-regularity constraints. In this paper, we prove a weaker version of a conjecture proposed by Qiao, Park, and Koolen on diameter…
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…