  We consider discrete nonlinear Schr\"odinger equations of n sites with
periodic boundary conditions. These equations have n branches of standing waves
that bifurcate from zero. Traveling waves appear as a symmetry-breaking from
the standing waves for different amplitudes. The bifurcation is proved using
the global Rabinowitz alternative in subspaces of symmetric functions. As
examples, we present applications to the Schr\"odinger and Saturable lattices.
