The paper presents development of the authors’ approach to visualization of graph models of various types based on the use of visualization metaphors and aimed at increasing cognitive clarity of these models. One of the key problems of this approach is investigated – namely, formalization of the process of constructing representation metaphors for graph models. Features of graph models that allow formalizing the process of their visualization are considered, the necessary terminology is introduced. A number of principles have been formulated that must be considered when forming metaphors for representing graph models. On the basis of the introduced principles, a general approach to the construction of representation metaphors for visualization of arbitrary graph models is proposed. The main ideas for applying the proposed approach are demonstrated by the example of a fuzzy cognitive map when constructing a metaphor for representing the results of its structure and target analysis. The directions of advanced research have been determined, within the framework of which it is planned to further formalize the approach in order to ensure the possibility of its software implementation. In the future, the presented approach can become an important component of an integrated approach to building a visualization mechanism for an arbitrary graph model, which provides support for efficient visual analysis throughout all stages of modeling.