Weighted Graph Vertices Ranking Using Absolute Potentials of Electric Circuit Nodes

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.