The subject of this article is to present the results of the analysis of the possibilities to create optimal third-degree Reference Graphs which may be used to model ICT networks. The first part discusses the causes for the interest in the subject of the thesis. Basic definitions and terms related to the analysed type of graphs describing ICT networks are given. The second part consists of the analysis of the possibilities to construct regular third-degree structures bases on the usage of one ring of the parameters typical for Reference Graphs. A method of conduct is presented and then used for checking the potential possibility to construct optimal graphs. In the subsequent chapter the results of analysis of the possibilities to create optimal third-degree graphs with a double ring is discussed. The paper is concluded by observations and conclusions resulting from the research.