Yeah it's not ideal. Also with the current preference for category theory it would probably make more sense to not phrase E as a subset of NxN but rather to def

Yeah it's not ideal. Also with the current preference for category theory it would probably make more sense to not phrase E as a subset of NxN but rather to define two functions pre: E -> N and post: E -> N. You could then choose to add labels as either an additional function label: E -> L, or as several graphs layered on top of one another (especially helpful when you view each graph as an arrow N -> N, which in turn makes more sense when you have several different classes of nodes). If anyone's interested I'm loosely basing this description on the description of petri nets as outlined in Tai-Danae Bradley's interesting (and readable) Applied Category Theory: https://arxiv.org/pdf/1809.05923.pdf https://arxiv.org/pdf/1809.05923.pdf