DYNAMICS OF CENTRALITY MEASURES OF RANDOM GRAPH MATHEMATICAL MODELS

Subject of Research.Simulation is one of the most powerful tools among information security provision measures in the design process of communication systems. As compared to other methods, it considers large-capacity communication systems, improves the quality of network resource management solutions and predicts more accurately their consequences. In this case, random graphs are the basic mathematical models for the analyzed systems. They provide fundamental understanding of the analyzed network properties and serve as the basis for simulation. With regard to the processing power high development rate for computers and simulation environments, the study of the topological properties of random graphs becomes especially urgent. It involves analyzing the probabilistic dynamics of centrality measures. Method.In the experiment we used centrality calculation methods for vertices and the graph as a whole based on the scientific apparatus of the graph theory. Comparison method based on span diagrams was used in the study of probabilistic dynamics of graph mathematical models. Main Results. We have studied the dynamics of centrality measures in the Erdös-Renyi random graph model, the Watts-Strogatz small world model and the freely scalable Barabashi-Albert model. The centrality measures of these models have been compared with a real network. We have made it clear that the topological properties of a real network are described by the Barabashi-Albert model to the fullest extent possible. The analysis of centrality measures presented in the paper gives the possibility to trace interconnections between the parameters of various graph models, that, in turn, can be used in the analysis of real networks. Practical Relevance.The obtained results can be applied in modeling of physical and social systems presented in the form of graphs. The paper findings are of interest for professionals involved in the analysis of networks in various fields of science and technology: sociology, medicine, physics and radio engineering.