Should I Bring A Graduation Gift?

A gift is not mandatory but also just because you are graduating this year as well does not mean that you can not give a gift.
A small token of appreciation may be acceptable . Maybe a small personalized gift or a gift certificate would be fine. It depends on how close you are to this classmate as to how much you would be willing to spend on this person.
I do not think there is a right or wrong answer to giving a gift, for that is exactly what it is, a gift, and people should not expect one.
Do whatever you feel comfortable with and goodluck!