  We argue that Josephson junction networks may be engineered to allow for the
emergence of new and robust quantum coherent states. We provide a rather
intuitive argument showing how the change in topology may affect the quantum
properties of a bosonic particle hopping on a network. As a paradigmatic
example, we analyze in detail the quantum and thermodynamic properties of
non-interacting bosons hopping on a comb graph. We show how to explicitly
compute the inhomogeneities in the distribution of bosons along the comb's
fingers, evidencing the effects of the topology induced spatial Bose-Einstein
condensation characteristic of the system. We propose an experiment enabling to
detect the spatial Bose-Einstein condensation for Josephson networks built on
comb graphs.
