Weighted Graph Vertices Ranking Using Absolute Potentials of Electric Circuit Nodes

Authors

  • Vitalia A. Khitraya Institute of Applied Mathematical Research, Karelian Research Center of the Russian Academy of Sciences; Petrozavodsk State University

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. Then the current is sequentially supplied to all vertices and each time the ranks of the vertices are determined in accordance with their potentials. It is also proposed to take into account the weights of the graph vertices, which allows you to include additional information in the analysis.

Keywords:

graph, centrality measure, ranking procedure, Kirchhoff's circuit laws, transportation network, electrical circuit model

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References

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Mazalov, V. V., Khitraya, V. A. (2023). Graph vertices ranking using absolute potentials of electric circuit nodes. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 19(2), 233–250 (in Russian).

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Published

2023-12-30

How to Cite

Khitraya, V. A. (2023). Weighted Graph Vertices Ranking Using Absolute Potentials of Electric Circuit Nodes. Contributions to Game Theory and Management, 16, 87–98. Retrieved from https://gametheory.spbu.ru/article/view/17711

Issue

Vol. 16 (2023)

Section

Articles

License

Articles of "Contributions to Game Theory and Management" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.