  We show that the influence of spin-orbit (SO) coupling on the weak
localization effect for electrons in graphene depends on the lack or presence
of z/-z symmetry in the system. While for z/-z asymmetric SO coupling,
disordered graphene should display a weak anti-localization behavior at lowest
temperature, z/-z symmetric coupling leads to an effective saturation of
decoherence time which can be partially lifted by an in-plane magnetic field,
thus, tending to restore the weak localization effect.
