A question on the graph induced by the transition function of a deterministic Turing machine
Not likely: almost every property of a Turing Machine is undecidable, and almost every property of a graph is decidable.

If you ignore tape contents, you don't have Turing machines, you have finite automata. But graphs can't really represent tape content. 

You can perform some trivial dead code analysis, but there may be unreachable states which are reachable in your graph.