Lin-Lu-Yau curvature is a notion of curvature on a finite connected simple graph with at least two vertices. For 
, let 
give mass 
to vertex 
and distribute the remaining mass equally among its neighbors.
For distinct vertices 
and 
, define
 |
where 
is graph distance and 
is the Wasserstein distance
for that distance. The Lin-Lu-Yau curvature is
 |
Zhou and Zhang (2026) proved that a graph with graph diameter at least 3 has edge connectivity 
, where
is its minimum vertex degree and 
is the minimum Lin-Lu-Yau curvature over edges.
For graph diameter 2, they proved 
.
