  Networks of coupled LC oscillators that do not share a common ground node are
studied. Both resistive coupling and inductive coupling are considered. For
networks under resistive coupling, it is shown that the oscillator-coupler
interconnection has to be bilayer if the oscillator voltages are to
asymptotically synchronize. Also, for bilayer architecture (when both resistive
and inductive couplers are present) a method is proposed to compute a
complex-valued effective Laplacian matrix that represents the overall coupling.
It is proved that the oscillators display synchronous behavior if and only if
the effective Laplacian has a single eigenvalue on the imaginary axis.
