Undirected graphs store only one set of edges. The implementation of the just makes it seem like two different copies :)
I'm not sure I understand your response. I was being sloppy and using edge and edge descriptor interchangeably (since there is no separate concept of an edge).
Edge, edge descriptor. Close enough. In an adjacency list (at least), an edge descriptor is actually based on a pair. This means that the out and in edge iterators can construct an edge descriptor such that source and target return reasonable answers without having to duplicate data.