Does wave-particle duality exist for gravitational waves? For electromagnetic waves there exists a wave/particle duality: light sometimes behaves as a wave, and other times as a particle (photons).
Does such a duality exist for gravitational waves? In other words would we expect gravitational waves to sometimes behave has particles (gravitons)?
 A: Yes. Gravitational waves have been observed, and assuming that quantum mechanics is the right way to think about the universe, then weak gravitational waves of the sort that can be observed at LIGO can be thought of as coherent ensembles of 'graviton' particles. 
Now, theoretically this picture is 'OK' because although any quantum field theory that describes gravity is nonrenormalizable, the energy scale at which we expect new physics associated with gravity to be detectable is extremely large ($\sim 10^{19} \text{GeV}$). Hence, we can use an effective theory valid at low energies to describe gravity in terms of particles, even if the 'true' theory of gravity valid at arbitrary energies or length scales is somewhat different conceptually.
Unfortunately, it's impossible with current technology to observe or manipulate single gravitons in a lab, so gravitons are still theoretical.
A: Although we lack the technology to observe gravitons, and our observation of gravitational waves is very recent and too early to absolutely confirm, gravitons should exist due to quantum theory which states that every elementary and undivisible particle does experience wave-particle duality.
