Modeling and Analysis of a Dynamic Network of Telephone Subscribers Considering the Degree of Connectivity by Means of Contact Lists

Abstract

Abstract. Modeling complex dynamic networks, whose components interact and evolve, is essential for understanding and predicting their behaviour. It helps to optimize performance, improve resilience, and effectively manage resources in technological, information, social, and biological networks. Purpose. The purpose of the work is to model a dynamic network of telephone subscribers, identify and evaluate its main properties. The focus is on experiments with the resulting model and determining the dependencies of network properties based on simulation data. Research methods. The methods of constructing computer models, methods of analyzing network parameters, the method of least squares and the Monte Carlo method of stochastic dynamics of discrete states by using time steps of equal length have been used in the work. The computer model has been developed in Python by using the Pandas, Numpy and NetworkX libraries. Results. A model of a dynamic network of telephone subscribers is proposed with imitation of contact lists, which usually include family members, colleagues, and friends. Experiments have been conducted with the model and the dependences of network properties on the number of subscribers and the fraction of contacts within contact lists have been investigated. The values of the model parameters at which the network exhibits the properties of a small-world network has been determined. Conclusions. The proposed model of a dynamic network of telephone subscribers with imitation of contact lists has allowed to identify the dependences of the network properties on the number of subscribers and the fraction of contacts within the contact lists. It was revealed that the node degree distribution corresponds to the lognormal law. The number of links in the call graph depends on the number of subscribers linearly, and the higher the fraction of contacts, the fewer links are created when a new subscriber appears. An increase in the number of subscribers affects the network density reducing it according to a hyperbolic law. As the fraction of contacts increases, the network density decreases, since an increasing number of connections are created among a limited number of subscribers. The clustering coefficient changes according to a hyperbolic law as well. The average value of the shortest path length for certain network parameters is well approximated by a logarithmic function when the fraction of contacts is more than 0.80 within contact lists. Finally, the qualities of a small-world network can be recognised in the dynamic network of telephone subscribers when the fraction of contacts in the contact list falls between 0.80 and 0.90, as determined by the coefficient ω (4).