Modified Mayerson value for determining the centrality of graph vertices

To analyze the structure of social networks, we can use methods of cooperative game theory. One of such methods is based on the calculation of the Myerson values as a measure of the centrality of the vertices in the 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. The paper proposes a modification of the Myerson value for the case when the paths in the graph containing cycles are included in the consideration. The effectiveness of this approach is shown on a number of examples.