  We investigate the entanglement of the ground state in the quantum networks
that their nodes are considered as quantum harmonic oscillators. To this aim,
the Schmidt numbers and entanglement entropy between two arbitrary partitions
of a network, are calculated. In partitioning an arbitrary graph into two parts
there are some nodes in each parts which are not connected to the nodes of the
other part. So these nodes of each part, can be in distinct subsets. Therefore
the graph separates into four subsets. The nodes of the first and last subsets
are those which are not connected to the nodes of other part. In theorem I, by
using generalized Schur complement method in these four subsets, we prove that
all graphs which their connections between all two alternative subsets are
complete, have the same entropy. A large number of graphs satisfy this theorem.
Then the entanglement entropy in the limit of large coupling and large size of
system, is investigated in these graphs. One of important quantities about
partitioning, is conductance of graph. The con- ductance of graph is considered
in some various graphs. In these graphs we compare the conductance of graph and
the entanglement entropy.
