Mazalov V.V., Khitraya V.A.
A Modified Myerson Value for Determining the Centrality of Graph Vertices
// Automation and Remote Control, v. 82, issue 1. 2021. P. 145–159
Keywords: graphs, paths with cycles, centrality measures, cooperative game, Myerson value
To analyze the structure of social networks, the methods of cooperative game theory can be adopted. One of such methods is based on the calculation of the Myerson values as a centrality measure of the vertices in a graph. In this case, the number of paths of a certain length in the subgraphs corresponding to the coalitions is used as the characteristic function. This paper proposes a modification of the Myerson value for the case where the paths in a graph containing cycles are included in consideration. The effectiveness of this approach is illustrated by several examples.
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