Under intense laser excitation, thin films and suspensions of graphite and its nanostructure, including carbon black, nanotubes, few-layer graphenes and graphene oxides, exhibit induced transparency due to saturable absorption. This switches to optical limiting only at very high fluences when induced breakdown gives rise to microbubbles and microplasmas that causes nonlinear scattering. Here, we show that dispersed graphenes, in contrast, can exhibit broadband nonlinear optical absorption at fluences well below this damage threshold with a strong matrix effect. We obtained, for nanosecond visible and near-infrared pulses, a new benchmark for optical energy-limiting onset of 10 mJ cm-2 for a linear transmittance of 70%, with excellent output clamping in both heavy-atom solvents and polymer film matrices. Nanosecond pump-probe spectroscopy in chlorobenzene reveals that the nanographene domains switch from the usual broadband photo-induced bleaching to a novel reverse saturable absorption mechanism with increasing excitation densities across this threshold.