## Portfolio item number 1

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Published in *Proceedings – 2017 Siberian Symposium on Data Science and Engineering, SSDSE 2017, 8071957, P.23-26. DOI: 10.1109/SSDSE.2017.8071957*, 2017

A random sampling of frames method, based on a statistical approach, and an algorithm to estimate the occurrence of 3-motifs in networks with directed links is proposed. We suggest implementing the algorithm with the help of parallel computing. The results of numerical data experiments are given. When comparing the developed algorithm with other known algorithms its significant advantages in terms of accuracy, speed and consumption of RAM are revealed in some cases.

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Published in *11th International IEEE Scientific and Technical Conference Dynamics of Systems, Mechanisms and Machines Dynamics. – P.1-8. DOI: 10.1109/Dynamics.2017.8239525*, 2017

A new class of graphs is introduced in preferential attachment random graphs theory, these graphs are grown by adding an infinite number of complex stochastic increments, consisting of several interconnected vertices. The problems of final degree distributions for vertices and edges of growing graphs are solved by analytic methods. Analytic solution of a graph calibration (synthesis) problem due to the given final degrees distribution of vertices and edges is derived. Numerical method is developed for a complex graph calibration by vertex degree distributions together with edge degrees and clustering coefficient. The examples of the complex graph calibration in real network modeling are given.

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Published in *Moscow Workshop on Electronic and Networking Technologies (MWENT), P. 1-7. DOI: 10.1109/MWENT.2018.8337251*, 2018

For growing graphs of preferential attachment that lose arcs continuously the problem of calculating the two-dimensional arcs (edges) degrees distribution is solved. The application of the developed methods for calculating graphs with arcs losses allows us to synthesize adequate models of growing networks (social, information-telecommunication, cooperation networks, etc.), taking into account the loss of connections between nodes.

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Published in *Journal of Physics: Conference Series, V. 1260, P. 022012*, 2019

The article deals with the problem of calculating the frequency of network motifs with a help of Rand-ESU algorithm. We have established that while using a Rand-ESU algorithm, it is necessary to cut off (to thin out) the network motifs only on the last level of ESU-tree (and therefore, an implementation of the algorithm requires the construction of almost entire ESU-tree). Examples of calculations are given, they demonstrate, that other strategies to cut-off sampling lead to larger distance errors in calculation.

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Published in *Journal of Physics: Conference Series, V. 1260, P. 022013*, 2019

The problem of calculating the frequencies of network motifs on three and four nodes in large networks is considered. Telecommunications networks, cell molecular networks are investigated. The sizes of the investigated networks are hundreds of thousands of nodes and connections. These networks are represented in the form of directed and undirected simple graphs. Exact calculating requires huge computational resources for such large graphs. A method for calculating the frequencies of network motifs using the Monte Carlo method with control of an accuracy of calculations is proposed. The proposed effective method minimizes the value of the coefficient of variation.

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Published in *Journal of Physics: Conference Series, V.1441, P. 012176*, 2020

The preferential attachment graphs are considered as the basis for constructing agent interaction structures. The choice of such a structure has a great influence on the results of network processes simulation. Calibration (adjusting generation parameters) of the preferential attachment graphs improves the accuracy of the simulated processes results. An increase in the quality of calibration leads to the construction of adequate graph models. It can be used in processes simulation of telecommunication networks, social networks, cell molecular networks and other large networks of the modern networked world.

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** Published:**

Undergraduate course, *University 1, Department*, 2014

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Workshop, *University 1, Department*, 2015

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