This is pretty cool! I probably would have never discovered graph-easy if it weren't for this.

One thing though, it doesn't handle errors that nicely, e.g. for input "a" it outputs "null". Nitpicking aside, it's neat.

Edit: I wonder what sort of heuristics graph-easy is using behind the scenes to decide where to place the clusters, etc., and how it can tell whether a particular input is feasible or not.