  The local complementation rule is applied for continuous-variable (CV) graph
states in the paper, which is an elementary graph transformation rule and
successive application of which generates the orbit of any graph states. The
corresponding local Gaussian transformations of local complementation for
four-mode unweighted graph states were found, which do not mirror the form of
the local Clifford unitary of qubit exactly. This work is an important step to
characterize the local Gaussian equivalence classes of CV graph states.
