  In this Note we investigate Bose-Einstein condensation in interacting quantum
many-particle systems on graphs. We extend previous results obtained for
particles on an interval and show that even arbitrarily small repulsive
two-particle interactions destroy a condensate in the non-interacting Bose gas.
Our results also cover singular two-particle interactions, such as the
well-known Lieb-Lininger model, in the thermodynamic limit.
