The bandgap at the K-points of undoped graphene is zero and the conduction and valence bands have conical form with the tips of the cones touching at the Fermi energy.  The density of states is zero because the cones touch at an infinitely small point that has no 'range' or 'extent' in E-k space. i.e. there are no states at this point and hence the density of states is zero.  The effective mass of the carriers is inversely proportional to the curvature of the E-k surface.  Since the curvature at a sharp point is infinite the effective mass is zero at the tip of the cones.  

https://www.youtube.com/watch?v=N4vzSKqyoIw

https://www.youtube.com/watch?v=gKlHL76BHc8

I think it is because graphene is a zero-bandgap semiconductor with bands intersecting at the Dirac points. Also, I think that since electrons and holes in graphene hold a linear dispersion relation with zero band gap might be the reason behind considering them as mass-less in graphene.

The bandgap at the K-points of undoped graphene is zero and the conduction and valence bands have conical form with the tips of the cones touching at the Fermi energy.  The density of states is zero because the cones touch at an infinitely small point that has no 'range' or 'extent' in E-k space. i.e. there are no states at this point and hence the density of states is zero.  The effective mass of the carriers is inversely proportional to the curvature of the E-k surface.  Since the curvature at a sharp point is infinite the effective mass is zero at the tip of the cones.