  New coherent states may be induced by pertinently engineering the topology of
a network. As an example, we consider the properties of non-interacting bosons
on a star network, which may be realized with a dilute atomic gas in a
star-shaped deep optical lattice. The ground state is localized around the star
center and it is macroscopically occupied below the Bose-Einstein condensation
temperature T_c. We show that T_c depends only on the number of the star arms
and on the Josephson energy of the bosonic Josephson junctions and that the
non-condensate fraction is simply given by the reduced temperature T/T_c.
