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 $p$-Ollivier curvature up to scaling whenever the idleness parameter $p\ge 1/2$. Mor…