Initially this should be zero. Process the top stack item, so long as the stack is not empty. If it has then the startVertex must be on a cycle. Start vertex shown to be reachable on a nontrivial cycle. Helper method to get the start vertex given the name.
Returns null if no such vertex exists.
Return null if the Graph is null. Helper method to initialize the search. Initialize the toDo stack of search items to be empty. Helper method to process the next item on the search's toDo stack. Process the first neighbour in this enumeration.