Cooper pairs localization in tree-like networks of superconducting islands

We study inhomogeneous Cooper pairs distribution and localization effects in tree-like networks of superconducting islands coupled via Josephson weak links. Using a generalized Feynman's approach, reminiscent of the Bose-Hubbard model, we demonstrate that the Cooper pairs fraction which localizes on a specific network's island is limited by the network topology and, if present, by the repulsive interaction. These findings contribute to clarify the interplay between confinement effects induced by the network's topology and interaction and shed some light on recent experiments dealing with networks of Josephson junctions.