The paper considers the model for controlling the dynamics of opinions in a society with infinite time horizon, and its modernization carried out for the possibility of transforming a network structure without affecting optimal control. The relation of the models with different network structures is investigated. Some particular graphs are defined and the ratio of parameters is shown. The ratio is at which a one-to-one correspondence between the models defined by these graphs is determined. The form of the functionals corresponding to these models and the ratio of the parameters for which the control problems are equivalent are obtained. Propositions about the correspondence between the models and about the equivalence of control problems are formulated, and the proofs of these propositions are given.