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References

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Published: January 23, 2020

Conferences 2020

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Published: January 01, 2020

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Agent-based Simbigraph modeling system

Mathematical models and numerical methods are implemented in periodically updated versions of the Simbigraph agent-based simulation system

Omsk state Technical University Scientist Collaboration Networks

WoS_2019

WoS_2020

Social network data collection and analysis

A number of projects to gathering data on social networks have been implemented. Large network analysis programs have also been developed.

publications

Structural properties of the scale-free Barabasi-Albert graph

Published in Automation and Remote Control, Vol. 73, No. 4, P. 702-716. DOI: 10.1134/ S0005117912040091, 2012

Consideration was given to the scale-free Barabasi-Albert graph describing large network structures of the Internet type. A fundamental graph matrix describing precisely the properties of the randomly selected edges was introduced and examined. The formula of the clustering coefficient was derived, and a method for its separable adjustment was proposed which does not affect the distribution of the local connectivity of vertices.

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Growing network: models following nonlinear preferential attachment rule

Published in Physica A: Statistical Mechanics and its Applications , 2015

We investigate the preferential attachment graphs proceeding from the following two assumptions. The first one: the probability that a new vertex connects to a vertex is proportional to an arbitrary nonnegative function of a vertex degree . The second assumption: a new vertex can have a random number of edges.

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Statistical approach to calculation of number of network motifs// 2015 International Siberian Conference on Control and Communications

Published in IEEE International Siberian Conference on Control and Communications, SIBCON 2015 – Proceedings P.7147296. DOI: 10.1109/SIBCON.2015.7147296, 2015

The article proposes to accelerate this process by using the Monte-Carlo method. Examples of counting of tgraphlets with 3 and 4 vertices are given. The proposed approach can also be extended to analysis of directed graphs

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Analytical and numerical methods of calibration for preferential attachment random graphs

Published in International Siberian Conference on Control and Communications (SIBCON). Proceedings, P. 7998461. DOI: 10.1109/SIBCON.2017.7998461, 2017

The methods of random graphs growing with nonlinear preferential attachment rule, which have the required distributions of vertices and edges attachment degrees are developed. Application of these methods allows us to generate random graphs, which adequately simulate growing stochastic networks - social, information, transport and many others. Examples of application for the developed methods are given.

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Calculation of number of motifs on three nodes using random sampling of frames in networks with directed links

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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Graphs with complex stochastic increments

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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The investigation of social networks based on multi-component random graphs

Published in J. Phys.: Conf. Ser. 944, P.012124. DOI: 10.1088/1742-6596/944/1/012124, 2018

The methods of non-homogeneous random graphs calibration are developed for social networks simulation. The graphs are calibrated by the degree distributions of the vertices and the edges. The mathematical foundation of the methods is formed by the theory of random graphs with the nonlinear preferential attachment rule and the theory of Erdôs-Rényi random graphs. In fact, well-calibrated network graph models and computer experiments with these models would help developers (owners) of the networks to predict their development correctly and to choose effective strategies for controlling network projects.

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Growing graphs with addition of communities

Published in Journal of Physics: Conference Series 1050(1), P. 012099. DOI: 10.1088/1742-6596/1050/1/012099, 2018

Paper proposes a model of large networks based on a random preferential attachment graph with addition of complete subgraphs (cliques). The proposed model refers to models of random graphs following the nonlinear preferential attachment rule, and takes into account the possibility of «adding» entire communities of nodes to the network. In the derivation of the relations that determine the vertex degree distribution, the technique of finite-difference equations describing stationary states of a graph is used. The obtained results are tested empirically (by generating large graphs), special cases correspond to known mathematical relations.

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Distributions of degrees in growing graphs with loss of arcs

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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Mixed Random Sampling of Frames method for counting number of motifs

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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