Adding a post because I lack the rep to comment.

There is at least one graph per language (assuming a language is a finite or countably infinite set of finite-length words). There will in fact be infinitely many graphs per language. You need to restrict the question further to have interesting answers. Your first question is about the graphs over a given alphabet whereas the comment later is about graphs per language. There are markedly different.

These pages may help (the latter two based on your tags).