graphs and networks - How can I remove B -> A from a list if A -> B is in the list?

I have a list of transformations like this:

list = {"A" -> "B", "B" -> "A", "C" -> "D"}

As this is used to plot an undirected graph with GraphPlot, I don't want to have an Edge between the vertices A-B and B-A. I just want one of them.

How do I remove either A -> B or B -> A from this list? In the end, I want the list to look like this:

{"A" -> "B", "C" -> "D"}

I've tried using DeleteDuplicates, but I don't think I understand the testing part of that function (I should add that I'm a Mathematica beginner ... )

I made a function that can compare two transformations:

CmpTrans[x_,y_] := (x[[1]]/.x) == y[[1]]

It returns True for CmpTrans[A->B, B->A], but I can't seem to use this is the testing part of DeleteDuplicates.

Answer

This seems to do what you want:

rules = {"A" -> "B", "B" -> "A", "C" -> "D"};

Rule @@@ Union[Composition[Sort, List] @@@ rules]
(* {"A" -> "B", "C" -> "D"} *)