what is the equivalence class of a given polytree representing a directed graphical model?
You can pick any other node as root and redirect nodes away from it to get Markov equivalent model. Markov equivalent means that two graphical models correspond to identical spaces of distributions.

Let "unshielded collider" be structure of the form A->B&lt;-C

Theorem: Two directed acyclic graphs D1 and D2 are Markov equivalent if and only if D1 and D2 have the same vertex set, same adjacencies, and same unshielded colliders.

See Ch.4 of Meek's "Related Graphical Frameworks: Undirected, Directed Acyclic and Chain Graph Models"
http://repository.cmu.edu/cgi/viewcontent.cgi?article=1206&amp;context=philosophy