This is more latex than lyx but I was hoping someone here knows the answer

I'm trying to see if it's possible to connect two points on the graph with the pgf fancy arrows from the shape library. That is
\node at (1,1) [double arrow, fill, color=green!70!black] {arrow};

I managed to put an arrow at a point (1,1 at the previous example) but I don't see how to get each end to rest at a give point (I need a path and not a point). Is it even possible, and if so, is it possible to do it with 90 degree bends? i.e

A
^
|
|
|--------B

Thanks

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