To have a graph, in general, you have to have multiple directed edges from a given object. A cons does not offer this, and the best you could do would be to treat cons cells in a extremely convoluted way as binary hypergraph nodes.
You said: "lisp represents graphs not lists". I think you meant that Lisp's defining data structure, based on the cons, was for general graphs, not lists. But that is not really true. If what you meant was "Lisp isn't just restricted to linked lists", sure, but that's true of every programming language with object arrays. So what?
Well, that's part of my point. However, in Lisp you get to macro the language into whatever you like, so you can make lisp into the desired graph language, layered on CONSs, but not so much with other languages because only in Lisp do you get to create an entirely new language. (People think of Lisp wrongly as a programming language, whereas it's really a meta-programming language.)
You said: "lisp represents graphs not lists". I think you meant that Lisp's defining data structure, based on the cons, was for general graphs, not lists. But that is not really true. If what you meant was "Lisp isn't just restricted to linked lists", sure, but that's true of every programming language with object arrays. So what?