  We have recently identified a protected topological semimetal in graphene
which presents a zero-energy edge mode robust to disorder and interactions.
Here, we address the characteristics of this semimetal and show that the
$\mathbb{Z}$ topological invariant of the Hall conductivity associated to the
lowest energy band can be equivalently measured from the resonant response to
circularly polarized light resolved at the Dirac points. The (non-quantized)
conductivity responses of the intermediate energy bands, including the Fermi
surface, also give rise to a $\mathbb{Z}_2$ invariant. We emphasize on the
bulk-edge correspondence as a half-topological protected semimetal, i.e. one
spin-population polarized in the plane is in the insulating phase related to
the robust edge mode while the other is in the metallic regime. The quantized
transport at the edges is also equivalent to a $\frac{1}{2}-\frac{1}{2}$
conductance for spin polarizations along $z$ direction. We also build a
parallel between the topological Hall response through the quantized light
response at the Dirac points and a pair of half numbers (half Skyrmions).
