  Graphene pn junction is the brick to build up variety of graphene
nano-structures. The analytical formula of the conductance of graphene gradual
pn junctions in the whole bipolar region has been absent up to now. In this
paper, we analytically calculated that pn conductance with the spin-orbit
coupling and stagger potential taken into account. Our analytical expression
indicates that the energy gap causes the conductance to drop a constant value
with respect to that without gap in a certain parameter region, and manifests
that the curve of the conductance versus the stagger potential consists of two
Gaussian peaks -- one valley contributes one peak. The latter feature allows
one to detect the valley polarization without using double-interface resonant
devices.
