We analyze the developing of bipartite and multipartite entanglement through the Mottinsulator–superfluid quantum phase transition. Starting from a Mott insulator state, where a fillingfactor ν = N/M = 1 per lattice site is considered, we derive an expression for a completely connected graphconfiguration of bosons and show how bipartite and multipartite entanglement evolvethrough the phase transition predicted in previous works. We show how, in the transition,bipartite entanglement is distributed through the system respecting monogamousrelations.