Wow, that looks crazy. I've never dealt with stuff like that before. I would go with what I know and try to put it in terms of some sort of algebra, but how to precisely do that translation is foreign to me.
Though, if I were to go that route, I would draw each graph using the same notation (0 through 9). From there I would specify each "joint" in terms of what it connects to. If they're isomorphic, we should see equivalent joints, right? (E.g., 1 is a joint on (2, 7, 9).)