Are you allowed to change the specifications of a problem when doing reductions?
It doesn't matter what B exactly is, it could be graph problem or something else. Nobody cares as long as you construct its instance in polynomial time and it has a solution precisely when the instance of A has. Maybe you need to use some structure of A to construct B, but maybe some parts of A don't need to be used at all, who knows.

So precisely what you must do is follow the definitions, and then everything is fair game with no authority setting any special rules.