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This paper is devoted to the existence of non-trivial bound states ofprescribed mass for the mass-supercritical nonlinear Schr\"odinger equation oncompact metric graphs. The investigation is based upon a general variationalprinciple which combines the monotonicity trick and a min-max theorem withsecond order information, and upon the blow-up analysis of bound states withprescribed mass and bounded Morse index.

Normalized solutions of $L^2$-supercritical NLS equations on compact metric graphs