User blog comment:Wythagoras/Friendship function/@comment-1605058-20140717204945

I must admit that the way you defined the function is extremely unintuitive - on one hand, it's really hard to work with just friendship graphs, because from the graph it's hard to figure out what bracket representation is. I can even justify use of word "hard" - finding the largest clique (that is, a complete subgraph) is an NP-hard problem, see Clique problem.

On the other hand, when we have to deal with bracket's only, it's another hard thing to tell if this is a proper friendship, i.e. if it represents any graph. I wouldn't be surprised if this turned out to be NP-hard as well. And, even if we know that given bracketing is a graph, it's quite difficult to figure out how many vertices it has.

It can or can be not strong system, but it certainly is not the system I'd prefer working with over SSCG.