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

Existence and multiplicity of peaked bound states for nonlinear Schr\"odinger equations on metric graphs