Network structures and systems: II. Network and multiplex cores

Authors

DOI:

https://doi.org/10.20535/SRIT.2308-8893.2018.3.04

Keywords:

complex network, network system, flow, multiplex, model, core, kernel

Abstract

The notion of the flow core of the network system is introduced and the functional advantages of its structure in comparison with the core of the complex network are analyzed. It has been shown that the flow cores allow us to construct a much more adequate with functional point of view the models of network systems than the cores of complex networks. This is demonstrated on the examples of practically important problems of controllability, observability and synchronization of complex networks. On the base of analysis of the structures of real systems, a generalized definition of the multiplex is proposed and the notion of its kernel is introduced. A few of modeling problems of multiplexes are considered and it is established that the effect of the "small world" in them increases. The flow adjacency matrix for the multiplex system is constructed. On its basis, a few of local and global characteristics of the multiplex system are determined and the properties of its flow core are investigated. Methods of reducing the dimension of models of multiplex systems with simultaneous monitoring of the quantitative measure of maintaining their adequacy are analyzed.

Author Biographies

O. D. Polishchuk, Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of the National Academy of Sciences of Ukraine, Lviv

Olexandr Polishchuk,

Ph.D. in Physics and Mathematics, a senior researcher in the Laboratory of Modeling and Optimization of Complex Systems of Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of the National Academy of Sciences of Ukraine, Lviv, Ukraine.

M. S. Yadzhak, Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of the National Academy of Sciences of Ukraine, Lviv

Mykhailo Yadzhak,

a senior researcher, Doctor of Sciences (Physics and Mathematics), the Head of the Laboratory of Modeling and Optimization of Complex Systems of Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of the National Academy of Sciences of Ukraine, Lviv, Ukraine.

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Published

2018-10-16

Issue

Section

Problem- and function-oriented computer systems and networks