  We investigate spin conductance in zigzag graphene nanoribbons and propose a
spin injection mechanism based only on graphitic nanostructures. We find that
nanoribbons with atomically straight, symmetric edges show zero spin
conductance, but nonzero spin Hall conductance. Only nanoribbons with
asymmetrically shaped edges give rise to a finite spin conductance and can be
used for spin injection into graphene. Furthermore, nanoribbons with rough
edges exhibit mesoscopic spin conductance fluctuations with a universal value
of $\mathrm{rms} G_\mathrm{s}\approx 0.4 e/4\pi$.
