Vestnik Sankt-Peterburgskogo Universiteta. Seriya 10. Prikladnaya Matematika. Informatika. Protsessy Upravleniya
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Vestnik Sankt-Peterburgskogo Universiteta. Seriya 10. Prikladnaya Matematika. Informatika. Protsessy Upravleniya, 2023, Volume 19, Issue 2, Pages 233–250
DOI: https://doi.org/10.21638/11701/spbu10.2023.209 (Mi vspui580) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Computer science

Graph vertices ranking using absolute potentials of electric circuit nodes

V. V. Mazalov, V. A. Khitraya

Federal Research Center “Karelian Research Center of the Russian Academy of Sciences’’, 11, Pushkinskaya ul., Petrozavodsk, Republic of Karelia, 185910, Russian Federation Petrozavodsk State University, 33, pr. Lenina, Petrozavodsk, Republic of Karelia, 185910, Russian Federation
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DOI: https://doi.org/10.21638/11701/spbu10.2023.209
Abstract: A method for ranking the vertices of a graph based on Kirchhoff's laws for determining the potentials of an electrical network is proposed. The graph is represented as an electrical network, where the edge weights are interpreted as electrical conductivities. Next, the current is supplied to one of the vertices, and the absolute potentials of all vertices are determined by the Kirchhoff method. Based on the obtained potential values, the vertices are ranked. Then the current is sequentially applied to all vertices and the ranking is performed each time. For the final ranking, it is proposed to apply the ranking procedure based on the tournament matrix. The operation of the ranking algorithm is illustrated by numerical examples related to graphs of specific transport networks.
Keywords: graph, centrality measure, ranking procedure, Kirchhoff's circuit laws, transportation network, electrical circuit model.
Funding agency Grant number
Russian Science Foundation 22-11-20015
The study was financially supported by the Russian Science Foundation (grant N 22-11-20015), conducted jointly with the authorities of the Republic of Karelia, and the Venture Investment Fund of the Republic of Karelia.
Received: March 4, 2023
Accepted: April 25, 2023
Document Type: Article
UDC: 519.178
MSC: 05C70
Language: Russian
Citation: V. V. Mazalov, V. A. Khitraya, “Graph vertices ranking using absolute potentials of electric circuit nodes”, Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 19:2 (2023), 233–250
Citation in format AMSBIB
\Bibitem{MazKhi23}
\by V.~V.~Mazalov, V.~A.~Khitraya
\paper Graph vertices ranking using absolute potentials of electric circuit nodes
\jour Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr.
\yr 2023
\vol 19
\issue 2
\pages 233--250
\mathnet{http://mi.mathnet.ru/vspui580}
\crossref{https://doi.org/10.21638/11701/spbu10.2023.209}
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Вестник Санкт-Петербургского университета. Серия 10. Прикладная математика. Информатика. Процессы управления
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