Conservation of connectivity of model-space effective interactions under a class of similarity transformation

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.