2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58144We consider free Bosons hopping on a network(infinite graph). The condition for Bose-Einstein condensation is given in terms of the random walk on a graph. In case of periodic lattices, we also consider Boson moving in an external periodic potential and obatined the criterion for Bose-Einstein condensation.Mathematical Physics82B10text