Centrality in directed social networks. A game theoretic approach

In this paper we define a family of centrality measures for directed social networks from a game theoretical point of view. We follow the line started in our previous paper (Gomez et al., 2003) and, besides the definition, we obtain a characterization of the measures and an additive decomposition in three summands that can be interpreted in terms of emission, betweenness and reception centrality components.

[1]  L. Freeman.  Centrality in social networks conceptual clarification , 1978 .

[2]  A. Nowak,et al.  The Shapley Value for n-Person Games in Generalized Characteristic Function Form , 1994 .

[3]  R. Brink.  An axiomatization of the disjunctive permission value for games with a permission structure , 1997 .

[4]  Frank Tutzauer,et al.  Entropy as a measure of centrality in networks characterized by path-transfer flow , 2007, Soc. Networks.

[5]  M. A. Beauchamp.  AN IMPROVED INDEX OF CENTRALITY. , 1965, Behavioral science.

[6]  G. Owen,et al.  The V L Value for Network Games , 2005 .

[7]  Peter Borm,et al.  Digraph Competitions and Cooperative Games , 2002 .

[8]  Gert Sabidussi,et al.  The centrality index of a graph , 1966 .

[9]  L. Shapley.  A Value for n-person Games , 1988 .

[10]  G. Owen,et al.  A game theoretic approach to measuring degree of centrality in social networks , 1982 .

[11]  R. Myerson.  Conference structures and fair allocation rules , 1978 .

[12]  P. Bonacich.  Factoring and weighting approaches to status scores and clique identification , 1972 .

[13]  U. J. Nieminen.  On the centrality in a directed graph , 1973 .

[14]  Alberto Leon-Garcia,et al.  Communication Networks , 2000 .

[15]  Gergely Palla,et al.  Centrality properties of directed module members in social networks , 2008, 0809.0669.

[16]  U. Faigle,et al.  The Shapley value for cooperative games under precedence constraints , 1992 .

[17]  Rafael Amer,et al.  Accessibility in oriented networks , 2007, Eur. J. Oper. Res..

[18]  Leonard M. Freeman,et al.  A set of measures of centrality based upon betweenness , 1977 .

[19]  Sergey Brin,et al.  The Anatomy of a Large-Scale Hypertextual Web Search Engine , 1998, Comput. Networks.

[20]  P. Bonacich.  Power and Centrality: A Family of Measures , 1987, American Journal of Sociology.

[21]  Peter Borm,et al.  Characterizations of the β- and the Degree Network Power Measure , 2008 .

[22]  M. Zelen,et al.  Rethinking centrality: Methods and examples☆ , 1989 .

[23]  Hans Peters,et al.  The selectope for cooperative games , 2000, Int. J. Game Theory.

[24]  S. Borgatti,et al.  Betweenness centrality measures for directed graphs , 1994 .

[25]  G. van der Laan,et al.  The Harsanyi set for cooperative TU-games , 2001 .

[26]  M. Slikker,et al.  Social and Economic Networks in Cooperative Game Theory , 2001 .

[27]  Henk Norde,et al.  Directed networks, allocation properties and hierarchy formation , 2005, Math. Soc. Sci..

[28]  René van den Brink,et al.  Measuring domination in directed networks , 2000, Soc. Networks.

[29]  Roger B. Myerson,et al.  Graphs and Cooperation in Games , 1977, Math. Oper. Res..

[30]  Alex Bavelas.  A Mathematical Model for Group Structures , 1948 .

[31]  G. Bergantiños,et al.  On values for generalized characteristic functions , 1997 .

[32]  Guillermo Owen,et al.  Centrality and power in social networks: a game theoretic approach , 2003, Math. Soc. Sci..

[33]  John C. Harsanyi,et al.  A Simplified Bargaining Model for the n-Person Cooperative Game , 1963 .

[34]  Peter Borm,et al.  The VL control measure for symmetric networks , 2009, Soc. Networks.

[35]  Francesc Llerena,et al.  The vector lattice structure of the n-person TU games , 2006, Games Econ. Behav..

[36]  G. Owen,et al.  Games with permission structures: The conjunctive approach , 1992 .

[37]  Stephen P. Borgatti,et al.  Centrality and network flow , 2005, Soc. Networks.