It really depends on how well you know these persons and the type and cost of said gifts. I think that the cost and level of intimacy of the gift should be commensurate with your familiarity with those who receiving the gifts. If these are friends, then giving gifts would be perfectly natural. If your relationship is a casual one, more on the level of acquaintances, then gifts might be perceived as somewhat awkward, especially extravagant ones. Even so, simple, inexpensive congratulatory gifts might not be amiss.
You have not given much information, but you do hint that they "do not feel the same way." If the relationship is not such that you feel they would consider giving you a gift if the situation were reversed, then it may not be a good idea to give them anything. What is your motivation for giving the gifts?
You said something about graduation, if you are all graduating together then you could give graduation gifts but only if that's what everyone else was doing and I'd still probably only do that with friends.
The only time's I would gift people I am not really friendly with would be at work if the person is leaving, or as a 'secret Santa' any other time it would just be seen as odd if you gifted someone you didn't really know very well, you can't buy friendship anyway.
I don't understand why simple innocent gifts are so odd. Gift giving is well documented throughout history and various cultures.
I am reminded of the scene where the boy brings the girl he likes a flower. I think they can be nice ice breakers and sweet gestures.
That being said, gifts bring subtext so that would need to be considered. The type of gift, the cost (if any) etc. Even things like flower species and color have meaning. You have to be careful when giving a gift, and it is especially interesting if you don't know the person, but that goes for anything you do to approach a person. If done well enough, a simple gift can be nice, to me.