On connected locally finite weighted graphs, the p-Ollivier curvature for p in [1/2,1] equals (1-p) times the Lin-Lu-Yau curvature, and 1/2 is the sharp threshold.
Minoux,Mathematical programming: theory and algorithms, John Wiley & Sons, 1986
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Equivalence of Lin--Lu--Yau curvature and 1/2-Ollivier curvature on weighted graphs
On connected locally finite weighted graphs, the p-Ollivier curvature for p in [1/2,1] equals (1-p) times the Lin-Lu-Yau curvature, and 1/2 is the sharp threshold.