  We study a set of $L$ spatial bosonic modes localized on a graph $\Gamma.$
The particles are allowed to tunnel from vertex to vertex by hopping along the
edges of $\Gamma.$ We analyze how, in the exact many-body eigenstates of the
system i.e., Bose-Einstein condensates over single-particle eigenfunctions, the
bi-partite quantum entanglement of a lattice vertex with respect to the rest of
the graph depends on the topology of $\Gamma.$
