使用电路节点的绝对电位对图顶点进行排序

IF 0.3 Q4 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya Pub Date : 2023-01-01 DOI:10.21638/11701/spbu10.2023.209

V. Mazalov, V. Khitraya

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引用次数: 0

摘要

提出了一种基于基尔霍夫定律确定电势的图顶点排序方法。图被表示为一个电网络，其中边的权重被解释为电导率。接下来，向其中一个顶点提供电流，并通过Kirchhoff方法确定所有顶点的绝对电位。根据获得的势值，对顶点进行排序。然后依次将当前值应用于所有顶点，并每次执行排序。对于最终的排名，建议采用基于比赛矩阵的排名程序。通过具体交通网络图的数值实例说明了排序算法的操作。

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Graph vertices ranking using absolute potentials of electric circuit nodes

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.

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来源期刊

Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

CiteScore

1.30

自引率

50.00%

发文量

期刊介绍： The journal is the prime outlet for the findings of scientists from the Faculty of applied mathematics and control processes of St. Petersburg State University. It publishes original contributions in all areas of applied mathematics, computer science and control. Vestnik St. Petersburg University: Applied Mathematics. Computer Science. Control Processes features articles that cover the major areas of applied mathematics, computer science and control.