Vine copulas is a way to represent multidimensional distributions (n-densitys) as a product of the n 1-marginal densities and a product of (n choose 2) bivariate copulas, where som of them are conditional. The most known vine copulas are canonical vines and D-vines. They can both be represented starting with a graph on n nodes, and connecting the nodes with a spanning tree with exactly (n-1) edges. In the case of a D-vine it is a linear tree, in the case of canonical vine it is a star.

This makes the following question natural: Is it possible to use every possible spanning tree to generate a valid vine? I did not encounter any counter-examples, but neither did I see a proof. Ideas?