  We investigate the bipartite entanglement for the boundary states in a simple
type of spin networks with dangling edges, in which the two complementary parts
are linked by two or more edges. Firstly, the spin entanglement is considered
in the absence of the intertwiner entanglement. By virtue of numerical
simulations, we find that the entanglement entropy usually depends on the group
elements. More importantly, when the intertwiner entanglement is taken into
account, we find that it is in general impossible to separate the total
entanglement entropy into the contribution from spins on edges and the
contribution from intertwiners at vertices. These situations are in contrast to
the case when the two vertices are linked by a single edge.
