Geodesic
Modified Mayerson value for determining the centrality of graph vertices
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 11 (2019) no. 2, pp. 19-39

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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.
Keywords: networks, paths with cycles, centrality measure, cooperative game, Myerson value. 
@article{MGTA_2019_11_2_a1,
     author = {Vladimir V. Mazalov and Vitaliya A. Khitraya},
     title = {Modified {Mayerson} value for determining the centrality of graph vertices},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {19--39},
     publisher = {mathdoc},
     volume = {11},
     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2019_11_2_a1/}
}
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Vladimir V. Mazalov; Vitaliya A. Khitraya. Modified Mayerson value for determining the centrality of graph vertices. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 11 (2019) no. 2, pp. 19-39. http://geodesic.mathdoc.fr/item/MGTA_2019_11_2_a1/