  We consider the ground-state entanglement in highly connected many-body
systems, consisting of harmonic oscillators and spin-1/2 systems. Varying their
degree of connectivity, we investigate the interplay between the enhancement of
entanglement, due to connections, and its frustration, due to monogamy
constraints. Remarkably, we see that in many situations the degree of
entanglement in a highly connected system is essentially of the same order as
in a low connected one. We also identify instances in which the entanglement
decreases as the degree of connectivity increases.
