Since I'm not an expert in graph theory, especially the arcane theory of "continuous graphs", your definition is unintuitive and excessively formal to me. How is that better? Abstractions are abstract. Almost no one learns purely by abstraction. Any definition must be accompanied by examples, and always is when taught.

Grouoa are taught in the context of addition/subtraction or permutations or symmetry groups, far more intuitive that graphs.