Light (massless particles/waves) cannot escape the gravity of a black hole. Gravitons travel at light speed and thus must be massless particles/waves. I can accept both postulates, but how do gravitons seem to defy their own gravity? This is what does not make sense to me.
Thanks!

We've never found a graviton or even proved one exists.
Not everyone thinks they do.
We can't explain why gravity is so weak, so we invented dark matter, which we also haven't found.
We believe black holes exist, but haven't really defined their properties since what Hawking postulated.
Maybe try this:
Everything You Know About Black Holes is Wrong | Quantum Mechanics of Black Holes | Space.com

PS: I am not a physicist. Hopefully someone(s) will figure this all out soon.

Couple of points. Gravitons are "virtual particles" under quantum gravity theory, and that theory has not been thoroughly thrashed out, so there's lots of speculation as to how they behave, or even if they exist at all. They are not part of general relativity, so are not be confined by GR constraints such as speed of light. The force of gravity that you feel is a manisfestation of the local curvature of space-time, so it's not that the black hole has to radiate anything - the curvature is all that is needed. By the way it's the same with electric fields - if the black hole carries an electric charge you can feel that as well.

@joypulv & ebaines: Thanks for the reply guys. Yes, true that the graviton is a theoretical particle. Perhaps I should have excluded it from my question. Thus, how then is a particle with no mass attracted by gravity? Or, to put it another way, why would a massless particle/wave have to follow the curve of space-time? I will check out the link on black holes, but in the meantime, isn't the fact that gravity doesn't act instantaneously but "travels" at the speed of light indirect proof that gravity is transmitted by a particle/wave and is not an "instant" field like a magnetic field? (Or do magnetic fields also not act instantaneously?)
Thanks!