Clusters of Exceedances for Evolving Random Graphs

Natalia M. Markovich; Maksim S. Ryzhov

doi:10.1007/978-3-031-23207-7_6

Clusters of Exceedances for Evolving Random Graphs

Natalia M. Markovich, Maksim S. Ryzhov

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Scopus citations

Abstract

Evolution of random undirected graphs by the clustering attachment (CA) without node and edge deletion and with uniform node deletion is investigated. The CA causes clusters of consecutive exceedances of the modularity over a sufficiently high threshold. The modularity is a measure that allows us to divide graphs into communities. It shows the connectivity of nodes in the community. An extremal index (a local dependence measure) approximates the mean cluster size of exceedances over a sufficiently high threshold. Considering the change of the modularity at each evolution step, the extremal index of the latter random sequence indicates the consecutive large connectivity of nodes and thus, it reflects the community appearance during the network evolution. This allows to consider the community structure of the network from perspectives of the extreme value analysis. By simulation study we show that estimates of the extremal index of the modularity and the tail index of node degrees depend on the CA parameters. The latter estimates are compared both for evolution without node and edge deletion and with uniform node deletion.

Original language	English
Title of host publication	Distributed Computer and Communication Networks
Subtitle of host publication	Control, Computation, Communications - 25th International Conference, DCCN 2022, Revised Selected Papers
Editors	Vladimir M. Vishnevskiy, Dmitry V. Kozyrev, Konstantin E. Samouylov
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	67-74
Number of pages	8
ISBN (Print)	9783031232060
DOIs	https://doi.org/10.1007/978-3-031-23207-7_6
State	Published - 1 Jan 2022
Externally published	Yes
Event	25th International Conference on Distributed and Computer and Communication Networks, DCCN 2022 - Moscow, Russian Federation Duration: 26 Sep 2022 → 29 Sep 2022

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	13766 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	25th International Conference on Distributed and Computer and Communication Networks, DCCN 2022
Country/Territory	Russian Federation
City	Moscow
Period	26/09/22 → 29/09/22

Keywords

Clustering attachment
Evolution
Extremal index
Modularity
Random graph
Tail index

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-031-23207-7_6

Cite this

Markovich, N. M., & Ryzhov, M. S. (2022). Clusters of Exceedances for Evolving Random Graphs. In V. M. Vishnevskiy, D. V. Kozyrev, & K. E. Samouylov (Eds.), Distributed Computer and Communication Networks: Control, Computation, Communications - 25th International Conference, DCCN 2022, Revised Selected Papers (pp. 67-74). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 13766 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-23207-7_6

Markovich, Natalia M. ; Ryzhov, Maksim S. / Clusters of Exceedances for Evolving Random Graphs. Distributed Computer and Communication Networks: Control, Computation, Communications - 25th International Conference, DCCN 2022, Revised Selected Papers. editor / Vladimir M. Vishnevskiy ; Dmitry V. Kozyrev ; Konstantin E. Samouylov. Springer Science and Business Media Deutschland GmbH, 2022. pp. 67-74 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "Evolution of random undirected graphs by the clustering attachment (CA) without node and edge deletion and with uniform node deletion is investigated. The CA causes clusters of consecutive exceedances of the modularity over a sufficiently high threshold. The modularity is a measure that allows us to divide graphs into communities. It shows the connectivity of nodes in the community. An extremal index (a local dependence measure) approximates the mean cluster size of exceedances over a sufficiently high threshold. Considering the change of the modularity at each evolution step, the extremal index of the latter random sequence indicates the consecutive large connectivity of nodes and thus, it reflects the community appearance during the network evolution. This allows to consider the community structure of the network from perspectives of the extreme value analysis. By simulation study we show that estimates of the extremal index of the modularity and the tail index of node degrees depend on the CA parameters. The latter estimates are compared both for evolution without node and edge deletion and with uniform node deletion.",

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Markovich, NM & Ryzhov, MS 2022, Clusters of Exceedances for Evolving Random Graphs. in VM Vishnevskiy, DV Kozyrev & KE Samouylov (eds), Distributed Computer and Communication Networks: Control, Computation, Communications - 25th International Conference, DCCN 2022, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 13766 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 67-74, 25th International Conference on Distributed and Computer and Communication Networks, DCCN 2022, Moscow, Russian Federation, 26/09/22. https://doi.org/10.1007/978-3-031-23207-7_6

Clusters of Exceedances for Evolving Random Graphs. / Markovich, Natalia M.; Ryzhov, Maksim S.
Distributed Computer and Communication Networks: Control, Computation, Communications - 25th International Conference, DCCN 2022, Revised Selected Papers. ed. / Vladimir M. Vishnevskiy; Dmitry V. Kozyrev; Konstantin E. Samouylov. Springer Science and Business Media Deutschland GmbH, 2022. p. 67-74 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 13766 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Ryzhov, Maksim S.

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N2 - Evolution of random undirected graphs by the clustering attachment (CA) without node and edge deletion and with uniform node deletion is investigated. The CA causes clusters of consecutive exceedances of the modularity over a sufficiently high threshold. The modularity is a measure that allows us to divide graphs into communities. It shows the connectivity of nodes in the community. An extremal index (a local dependence measure) approximates the mean cluster size of exceedances over a sufficiently high threshold. Considering the change of the modularity at each evolution step, the extremal index of the latter random sequence indicates the consecutive large connectivity of nodes and thus, it reflects the community appearance during the network evolution. This allows to consider the community structure of the network from perspectives of the extreme value analysis. By simulation study we show that estimates of the extremal index of the modularity and the tail index of node degrees depend on the CA parameters. The latter estimates are compared both for evolution without node and edge deletion and with uniform node deletion.

AB - Evolution of random undirected graphs by the clustering attachment (CA) without node and edge deletion and with uniform node deletion is investigated. The CA causes clusters of consecutive exceedances of the modularity over a sufficiently high threshold. The modularity is a measure that allows us to divide graphs into communities. It shows the connectivity of nodes in the community. An extremal index (a local dependence measure) approximates the mean cluster size of exceedances over a sufficiently high threshold. Considering the change of the modularity at each evolution step, the extremal index of the latter random sequence indicates the consecutive large connectivity of nodes and thus, it reflects the community appearance during the network evolution. This allows to consider the community structure of the network from perspectives of the extreme value analysis. By simulation study we show that estimates of the extremal index of the modularity and the tail index of node degrees depend on the CA parameters. The latter estimates are compared both for evolution without node and edge deletion and with uniform node deletion.

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T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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Markovich NM, Ryzhov MS. Clusters of Exceedances for Evolving Random Graphs. In Vishnevskiy VM, Kozyrev DV, Samouylov KE, editors, Distributed Computer and Communication Networks: Control, Computation, Communications - 25th International Conference, DCCN 2022, Revised Selected Papers. Springer Science and Business Media Deutschland GmbH. 2022. p. 67-74. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-031-23207-7_6