Given a directed graph $G\langle V,E\rangle$, and weight $w[u][v]$ of each $\langle u,v \rangle$ representing an edge of $E$ the question is, try to divide the whole graph into several "rings", making each vertex $u$ belong to a certain "ring" and a "ring" contains at least two vertices, it's guaranteed that the given graph must be able to be divided, satisfying the restrictions.
Finally, please make the total weight of all the "ring"s minimum .
This is a task assigned by my tutor, I don't know if it's an old problem because I'm new on algorithm, my tutor told me that it could be solved within polynomial time complexity, I wanna know how it can be done, I just have no idea about that...
PS: I'm terribly sorry for my forgetting to post the correct question at the first time...