  We study both analytically and numerically the existence, uniqueness, and
stability of vortex and dipole vector solitons in a saturable nonlinear medium
in (2+1) dimensions. We construct perturbation series expansions for the vortex
and dipole vector solitons near the bifurcation point where the vortex and
dipole components are small. We show that both solutions uniquely bifurcate
from the same bifurcation point. We also prove that both vortex and dipole
vector solitons are linearly stable in the neighborhood of the bifurcation
point. Far from the bifurcation point, the family of vortex solitons becomes
linearly unstable via oscillatory instabilities, while the family of dipole
solitons remains stable in the entire domain of existence. In addition, we show
that an unstable vortex soliton breaks up either into a rotating dipole soliton
or into two rotating fundamental solitons.
