Gravitons are predicted in Einstein's theory to be massless and to travel at the speed of light. Nevertheless, whether or not gravitons are masslesss is an open issue. Recently, Brito, Cardoso and Pani used observations of supermassive black holes to strongly constrain the graviton mass. Their calculations predicts that the graviton is lighter than 5x10^(-23)eV, or 10^(-55) grams. This new bound will feature in the Reviews of Particle Physics, and can be acessed here.
Reference: http://arxiv.org/abs/1304.6725