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Centrality and power in social networks: a game theoretic approach

Gómez, Daniel and González-Arangüena, Enrique and Conrado, Manuel and Owen, Guillermo and Pozo Juan, Mónica del and Tejada Cazorla, Juan Antonio (2003) Centrality and power in social networks: a game theoretic approach. Mathematical Social Sciences, 46 (1). pp. 27-54. ISSN 0165-4896

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Abstract

A new family of centrality measures, based on game theoretical concepts, is proposed for social networks. To reflect the interests that motivate the interactions among individuals in a network, a cooperative game in characteristic function form is considered. From the graph and the game, the graph-restricted game is obtained. Shapley value in a game is considered as actor's power. The difference between actor's power in the new game and his/her power in the original one is proposed as a centrality measure. Conditions are given to reach some desirable properties. Finally, a decomposition is proposed.


Item Type:Article
Uncontrolled Keywords:Social networks; Game theory; Centrality; Shapley value
Subjects:Sciences > Mathematics > Operations research
ID Code:15931
References:

Banzhaf, J., 1965.Weighted voting doesn’t work; a mathematical analysis. Rutger’s Law Review 19, 317–343.

Bavelas, A., 1948. A mathematical model for small group structures. Human Organization 7, 16–30.

Beauchamp, M.A., 1965. An improved index of centrality. Behavioral Science 10, 161–163.

Bonacich, P., 1972. Factoring and weighting approaches to status scores and clique identification. Journal of Mathematical Sociology 2, 113–120.

Bonacich, P., 1987. Power and centrality: a family of measures. American Journal of Sociology 92,1170–1182.

Dubey, P., Neyman, A., Weber, R.J., 1981. Value theory without efficiency. Mathematics of Operations Research 6, 122–128.

Freeman, L.C., 1977. A set of measures of centrality based on betweenness. Sociometry 40, 35–41.

Freeman, L.C., 1979. Centrality in social networks: conceptual clarification. Social Networks 1, 215–239

Grofman, B., Owen, G., 1982. A game theoretic approach to measuring centrality in social networks. Social Networks 4, 213–224.

Hanneman, R.A., 1999. Introduction to Social Network Methods (on-line textbook).

Mizruchi, M.S., Potts, B.B., 1998. Centrality and power revisited: actor success in group decision making. Social Networks 20, 353–387.

Myerson, R.B., 1977. Graphs and cooperation in games. Mathematics of Operation Research 2, 225–229.

Nieminen, J., 1974. On centrality in a graph. Scandinavian Journal of Psychology 15, 322–336.

Owen, G., 1986. Values of graph-restricted games. SIAM Journal on Algebraic and Discrete Methods 7,210–220.

Sabidussi, G., 1966. The centrality index of a graph. Psychometrika 31, 581–603.

Shaw, M.E., 1954. Group structure and the behaviour of individuals in small groups. Journal of Psychology 38,139–149.

Shapley, L.S., 1953. A value for n-person games. In: Tucker, A.W., Kuhn, H. (Eds.), Contributions to the Theory of Games II. Annals of Mathematics Studies,Vol. 28. Princeton University Press, Princeton, NJ, pp.307–317.

Shapley, L., Shubik, M., 1954. A method for evaluating the distribution of power in a committee system. American Political Science Review 48, 787–792.

Stephenson, K., Zelen, M., 1989. Rethinking centrality: methods and examples. Social Networks 11, 1–37.

Deposited On:12 Jul 2012 11:49
Last Modified:06 Feb 2014 10:34

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