  We establish existence and multiplicity of one-peaked and multi-peaked
positive bound states for nonlinear Schr\"odinger equations on general compact
and noncompact metric graphs. Precisely, we construct solutions concentrating
at every vertex of odd degree greater than or equal to $3$. We show that these
solutions are not minimizers of the associated action and energy functionals.
To the best of our knowledge, this is the first work exhibiting solutions
concentrating at vertices with degree different than $1$. The proof is based on
a suitable Ljapunov-Schmidt reduction.
