Wouldn't the Data.Graph.Inductive representation of a graph satisfy this (It might not be O(1), but it's pretty close)? I must admit that I find it hard to see what a zipper for a graph should look like, though.
You already know how a zipper for a tree looks like. And you have probably seen a functional queue. Generalizing from both of those, you can imagine how a zipper would work.
I can write down the types and all, even if I don't know of any implementation. But that's probably a topic for a blog post, or so.
The types I was talking about go as: type Context a b = (Adj b, Node, a, Adj b) type Adj b = [(b, Node)]
It definitely allows traversal, and adding nodes seems to be possible, too (judging from the api, of course, it ought to be :)