Modeling and Analyzing the Simplest Network of Telephone Subscribers

doi:10.26565/2304-6201-2023-59-01

Mykhailo Danilevskyi V.N. Karazin Kharkiv National University, Svobody Square, 4, Kharkiv-22, Ukraine, 61022 https://orcid.org/0009-0000-0030-2218
Volodymyr Yanovsky V. N. Karazin Kharkiv National University, sq. Svobody 4, Kharkiv, Ukraine, 61000; Institute of Single Crystals, National Academy of Sciences of Ukraine, Nauki Ave. 60, Kharkiv, Ukraine, 61001 https://orcid.org/0000-0003-0461-749X

DOI: https://doi.org/10.26565/2304-6201-2023-59-01

Keywords: dynamic complex network, mobile call graph, telephone network, lognormal distribution, degree distribution, network density, clustering coefficient, average shortest path length

Abstract

Abstract. Dynamic networks such as social, transport and biological networks are widely represented in the modern world. Modeling complex networks as time-varying structures opens up additional opportunities for studying their properties.

Purpose. The goal of the work is to model the simplest dynamic network of telephone subscribers. The main focus is on experiments with the resulting model and studying how the number of subscribers influences the network properties.

Research methods. The work uses the Monte Carlo method of stochastic dynamics of discrete states using time steps of the same length, as well as the methods for constructing computer models, the methods for analyzing the properties of networks, the least squares method and others. The computer model has been developed in Python using the Pandas, Numpy and NetworkX libraries.

Results. The simplest model of a network of telephone subscribers has been designed, where subscribers are connected randomly and disconnected after the phone conversation. In the model, the average daily number of outgoing calls from subscribers is distributed according to the lognormal law. The experiments have been carried out with different numbers of subscribers, but for the same time period. Based on the data obtained from the experiments, we analyzed such network properties as number of connections, density, degree distribution, average clustering coefficient, and average shortest path length.

Conclusions. The developed computer model of the simplest dynamic network of telephone subscribers forms a model similar to a random Erdes-Rényi graph, but the degrees of the vertices or the number of connections between subscribers are distributed according to a lognormal law. The developed computer model can serve as the basis for the development of more complex models and the study of the dynamic properties of such networks.

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Author Biographies

Mykhailo Danilevskyi, V.N. Karazin Kharkiv National University, Svobody Square, 4, Kharkiv-22, Ukraine, 61022

PhD student

Volodymyr Yanovsky , V. N. Karazin Kharkiv National University, sq. Svobody 4, Kharkiv, Ukraine, 61000; Institute of Single Crystals, National Academy of Sciences of Ukraine, Nauki Ave. 60, Kharkiv, Ukraine, 61001

Doctor of Physical and Mathematical Sciences, professor

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