This animation shows the Fermi surface of graphene for different dopings. The left panel shows the Brioullin zone in the k-space and the Fermi surfaces. The left panel shows the density of states and the right one the dispersion of graphene. The different doping levels are depicted as a line at the Fermi energy moving up in the dispersion and density of states.
One can nicely see the disappearence of the Fermi surface around the K points (corners of the Brillouin zone) for neutral Graphene (zero Fermi energy). In the parabolic regions of the dispersion, near the Gamma point for very low and very high dopings, the Fermi surface is a circle in very good approximation. In between the circular Fermi surface and the dot like Fermi surface, it has a triangular shape around the K points. Another interesting point to note is the fact that the Fermi surface changes its center from the Gamma point to the K point right at the van Hove singularities at 
The dispersion is calculated by the nearest neighbor tight-binding approximation, c.f. Rev. Mod. Phys. 81, 109