  Effective interaction operators usually act on a restricted model space and
give the same energies (for Hamiltonian) and matrix elements (for transition
operators etc.) as those of the original operators between the corresponding
true eigenstates. Various types of effective operators are possible. Those well
defined effective operators have been shown being related to each other by
similarity transformation. Some of the effective operators have been shown to
have connected-diagram expansions. It is shown in this paper that under a class
of very general similarity transformations, the connectivity is conserved. The
similarity transformation between hermitian and non-hermitian
Rayleigh-Schr\"{o}dinger perturbative effective operators is one of such
transformation and hence the connectivity can be deducted from each other.
