  We study discrete vortices in the anti-continuum limit of the discrete
two-dimensional nonlinear Schr{\"o}dinger (NLS) equations. The discrete
vortices in the anti-continuum limit represent a finite set of excited nodes on
a closed discrete contour with a non-zero topological charge. Using the
Lyapunov-Schmidt reductions, we find sufficient conditions for continuation and
termination of the discrete vortices for a small coupling constant in the
discrete NLS lattice. An example of a closed discrete contour is considered
that includes the vortex cell (also known as the off-site vortex). We classify
the symmetric and asymmetric discrete vortices that bifurcate from the
anti-continuum limit. We predict analytically and confirm numerically the
number of unstable eigenvalues associated with various families of such
discrete vortices.
