If it is in the same class it is fine to trust the method.
It is very common to do this. It is good practice to check null values in constructor's and method's arguments to make sure that nobody is passing null values into them (if it is not allowed). Then if you implement your methods in a way that they never set the "start" graph to null, don't check for nulls there.
It is also good practice to implement unit tests for your methods and make sure that they are correctly implemented, so you can trust them.