Estimation of the Tail Index of PageRanks in Random Graphs

Natalia M. Markovich; Maksim S. Ryzhov

doi:10.1007/978-3-031-23207-7_7

Estimation of the Tail Index of PageRanks in Random Graphs

Natalia M. Markovich
, Maksim S. Ryzhov

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

Abstract

Superstar nodes to which a large proportion of nodes attach in the evolving graphs are considered. We attract results of the extreme value theory regarding sums and maxima of non-stationary random length sequences to predict the tail index of the PageRanks and Max-linear models as influence measures of superstar nodes. To this end, the graphs are divided into mutually weakly dependent communities. Maxima and sums of the PageRanks over communities are used as weakly independent block-data. Tail indices of the block-maxima and block-sums and hence, of the PageRanks and the Max-linear models are found to be close to the minimum tail index of series of representative nodes taken from the communities. The graph evolution is provided by a linear preferential attachment. The tail indices are estimated by data of simulated and real temporal graphs.

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	75-89
Number of pages	15
ISBN (Print)	9783031232060
DOIs	https://doi.org/10.1007/978-3-031-23207-7_7
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

Community
Evolution
Max-linear model
PageRank
Preferential attachment
Random graph
Superstar node
Tail index

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-031-23207-7_7

Cite this

Markovich, N. M., & Ryzhov, M. S. (2022). Estimation of the Tail Index of PageRanks in 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. 75-89). (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_7

Markovich, Natalia M. ; Ryzhov, Maksim S. / Estimation of the Tail Index of PageRanks in 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. 75-89 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "Superstar nodes to which a large proportion of nodes attach in the evolving graphs are considered. We attract results of the extreme value theory regarding sums and maxima of non-stationary random length sequences to predict the tail index of the PageRanks and Max-linear models as influence measures of superstar nodes. To this end, the graphs are divided into mutually weakly dependent communities. Maxima and sums of the PageRanks over communities are used as weakly independent block-data. Tail indices of the block-maxima and block-sums and hence, of the PageRanks and the Max-linear models are found to be close to the minimum tail index of series of representative nodes taken from the communities. The graph evolution is provided by a linear preferential attachment. The tail indices are estimated by data of simulated and real temporal graphs.",

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Markovich, NM & Ryzhov, MS 2022, Estimation of the Tail Index of PageRanks in 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. 75-89, 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_7

Estimation of the Tail Index of PageRanks in 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. 75-89 (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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N2 - Superstar nodes to which a large proportion of nodes attach in the evolving graphs are considered. We attract results of the extreme value theory regarding sums and maxima of non-stationary random length sequences to predict the tail index of the PageRanks and Max-linear models as influence measures of superstar nodes. To this end, the graphs are divided into mutually weakly dependent communities. Maxima and sums of the PageRanks over communities are used as weakly independent block-data. Tail indices of the block-maxima and block-sums and hence, of the PageRanks and the Max-linear models are found to be close to the minimum tail index of series of representative nodes taken from the communities. The graph evolution is provided by a linear preferential attachment. The tail indices are estimated by data of simulated and real temporal graphs.

AB - Superstar nodes to which a large proportion of nodes attach in the evolving graphs are considered. We attract results of the extreme value theory regarding sums and maxima of non-stationary random length sequences to predict the tail index of the PageRanks and Max-linear models as influence measures of superstar nodes. To this end, the graphs are divided into mutually weakly dependent communities. Maxima and sums of the PageRanks over communities are used as weakly independent block-data. Tail indices of the block-maxima and block-sums and hence, of the PageRanks and the Max-linear models are found to be close to the minimum tail index of series of representative nodes taken from the communities. The graph evolution is provided by a linear preferential attachment. The tail indices are estimated by data of simulated and real temporal graphs.

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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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PB - Springer Science and Business Media Deutschland GmbH

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Y2 - 26 September 2022 through 29 September 2022

ER -

Markovich NM, Ryzhov MS. Estimation of the Tail Index of PageRanks in 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. 75-89. (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_7