  We consider the Schroedinger equation with a subcritical focusing power
nonlinearity on a noncompact metric graph, and prove that for every finite edge
there exists a threshold value of the mass, beyond which there exists a
positive bound state achieving its maximum on that edge only. This bound state
is characterized as a minimizer of the energy functional associated to the NLS
equation, with an additional constraint (besides the mass prescription): this
requires particular care in proving that the minimizer satisfies the
Euler--Lagrange equation. As a consequence, for a sufficiently large mass every
finite edge of the graph hosts at least one positive bound state that, owing to
its minimality property, is orbitally stable.
