  The scaling of entanglement entropy for the nearest neighbor
antiferromagnetic Heisenberg spin model is studied computationally for clusters
joined by a single bond. Bisecting the balanced three legged Bethe Cluster,
gives a second Renyi entropy and the valence bond entropy which scales as the
number of sites in the cluster. For the analogous situation with square
clusters, i.e. two $L \times L$ clusters joined by a single bond, numerical
results suggest that the second Renyi entropy and the valence bond entropy
scales as $L$. For both systems, the environment and the system are connected
by the single bond and interaction is short range. The entropy is not constant
with system size as suggested by the area law.
