You don't need a massive amount of graph theory. "Rearrange the labels of the graph so that the new graph looks the same as the old one" isn't exactly arcane, is it?
Abstractions are something that works great when you worked enough with some class of specific problems, that your brain notices common parts on its own. If you try to rush it... you get another tutorial when author is enthusiastic and positive and readers feel ashamed and stupid that they "couldn't get it". I'd rather avoid that. If they get foundations, play with them and gain some confidence, they can move on to more challenging and generic definitions.