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.