User blog comment:Wythagoras/Friendship function/@comment-1605058-20140717170937

As I expected, your friendship bracketing isn't able to differ all possible graphs. When I'm back home I'll provide explicit example of this. This is a problem because, in sequence for SSCG there may appear graphs disallowed by friendship minors.

Also, you have not specified order in which friendship brackets are written, thus allowing for multitude of bracket representations for same friendship combination.