  We present a robust and exact method for calculating the polarization
function and plasmon dispersion of graphene, for an arbitrary (isotropic)
non-equilibrium carrier distribution, within random phase approximation (RPA).
This is demonstrated for a range of carrier distributions, including hot
carrier distributions which occur within the femtoseconds following
photoexcitation. We show that qualitatively different behaviour from the
equilibrium case can occur. As the polarization function determines dynamic
screening, its calculation shall be essential to quantifying carrier-carrier
scattering channels for graphene far from equilibrium.
