Dynamics of entanglement of bosonic modes on symmetric graphs

We investigate the dynamics of an initially disentangled Gaussian state on a general finite symmetric graph. As concrete examples we obtain properties of this dynamics on mean field graphs (also called fully connected or complete graphs) of arbitrary sizes. In the same way that chains can be used for transmitting entanglement by their natural dynamics, these graphs can be used to store entanglement. We also consider two kinds of regular polyhedron which show interesting features of entanglement sharing.