#### For citation:

Pitsik E. N., Goremyko M. V., Makarov V. V., Hramov A. E. Mathematical modelling of the network of professional interactions. *Izvestiya VUZ. Applied Nonlinear Dynamics*, 2018, vol. 26, iss. 1, pp. 21-32. DOI: 10.18500/0869-6632-2018-26-1-21-32

# Mathematical modelling of the network of professional interactions

Description of real-world systems of interacting units by the means of network model is an effective method of research both in macro- and microscale. In addition, using the simple onelayer networks with one type of connections between the nodes when describing real-world networks is inefficiently because of their complex structural and dynamical nature. Besides, presence of similar features in real networks that are fundamentally different by their nature provided a wide spread of proposed model in many fields of science for the acquisition of new fundamental knowledge about functioning of the real network structures. For this reason the object of this article is modelling of multiplex network build on the basis of real data about professional interactions in world-wide musical community. The changes in characteristics in in proposed model reflects structural and dynamical features of real network, such as scale-free connection structure and clusters formation. Results obtained for multiplex network shows that after uniting the isolated systems their topologies undergo noticeable changes. In particular, significant changes in centrality values and in cluster formation inside the network were obtained. Besides, the correlations between the characteristics and dynamics of these correlations in process of uniting the isolated systems in general network. Obtained results confirm the effectiveness of multiplex network model for studying structural and dynamical processes of many real systems.

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