The subset of R³ realizing metrics on the curve complex

For each point V, a subset of R³, we define a distance on the one skeleton of curve complex for each point and prove that (1) for each point in V with all positive entries, the one skeleton of curve complex under this distance is a metric space and δ-hyperbolic for some δ∈R⁺; (2) for each point in V with at least one non-positive entry, the diameter of vertices of curve complex under this distance is finite.