Network Evolution Model with Preferential Attachment at Triadic Formation Step

Sergei Sidorov (), Timofei Emelianov, Sergei Mironov, Elena Sidorova, Yuri Kostyukhin, Alexandr Volkov, Anna Ostrovskaya and Lyudmila Polezharova
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Sergei Sidorov: Faculty of Mathematics and Mechanics, Saratov State University, 410012 Saratov, Russia
Timofei Emelianov: Faculty of Computer Science and Informatics, Saratov State University, 410012 Saratov, Russia
Sergei Mironov: Faculty of Computer Science and Informatics, Saratov State University, 410012 Saratov, Russia
Elena Sidorova: Faculty of Tax, Audit and Business Analysis, Financial University under the Government of the Russian Federation, 125993 Moscow, Russia
Yuri Kostyukhin: Engineering Business and Management Faculty, Bauman Moscow State Technical University, 105005 Moscow, Russia
Alexandr Volkov: Educational and Methodological Department, National University of Science & Technology (MISIS), 119049 Moscow, Russia
Anna Ostrovskaya: Higher School of Management, Peoples’ Friendship University of Russia (RUDN University), 117198 Moscow, Russia
Lyudmila Polezharova: Faculty of Tax, Audit and Business Analysis, Financial University under the Government of the Russian Federation, 125993 Moscow, Russia

Mathematics, 2024, vol. 12, issue 5, 1-21

Abstract: It is recognized that most real systems and networks exhibit a much higher clustering with comparison to a random null model, which can be explained by a higher probability of the triad formation—a pair of nodes with a mutual neighbor have a greater possibility of having a link between them. To catch the more substantial clustering of real-world networks, the model based on the triadic closure mechanism was introduced by P. Holme and B. J. Kim in 2002. It includes a “triad formation step” in which a newly added node links both to a preferentially chosen node and to its randomly chosen neighbor, therefore forming a triad. In this study, we propose a new model of network evolution in which the triad formation mechanism is essentially changed in comparison to the model of P. Holme and B. J. Kim. In our proposed model, the second node is also chosen preferentially , i.e., the probability of its selection is proportional to its degree with respect to the sum of the degrees of the neighbors of the first selected node. The main goal of this paper is to study the properties of networks generated by this model. Using both analytical and empirical methods, we show that the networks are scale-free with power-law degree distributions, but their exponent γ is tunable which is distinguishable from the networks generated by the model of P. Holme and B. J. Kim. Moreover, we show that the degree dynamics of individual nodes are described by a power law.

Keywords: triadic closure; social networks; preferential attachment; complex networks; high clustering; growth model; community structure; edge clustering (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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