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Centrality in social networks: Conceptual clarification. Social Networks 1(3), 215–239 (1979) 5. : Power indices. C. ) Wiley Encyclopedia of Operations Research and Management Science, vol. 8, John Wiley & Sons (2011) 6. : Recall versus recognition: Comparison of two alternative procedures for collecting social network data. , Kramberger, T. ) Proceedings of the International Conference on Methodology and Statistics, pp. 121–128 (1992, 1993) ´ Maximizing the spread of influence through 7. : a social network.

2 0 5 10 15 20 25 Girls Fig. 3. Comparative between Bz-C3, SS-C3, CC and CB for Dining-table partners (C1) minimum, f (i) = 1; (C2) average, f (i) = 2; and (C3) maximum, f (i) = 3. Unlike in the previous network, here there are no isolated nodes, but we can still obtaining scores for Bz and SS equal to zero. See the columns of Bz-C1 and SS-C1 on Table 2. − does not provide any relevant information, because Indegree centrality CD the indegree for each node is always 2 (see Table 2 and Figure 3).

Note that every simple game is an influence game [10]. From now on, we assume N = V and n = |N | = |V |. 2 Power Indices and New Centrality Measures A power index is a measure of the relevance of the players in a game [1,5]. We consider the two main power indices of a given simple game (N, W). The Banzhaf index Bz(i) = |Ci |/ i∈N |Ci | and the Shapley-Shubik index SS(i) = ( S∈Ci (|S| − 1)! , where Ci = {S ∈ W | S\{i} ∈ / W}. Power indices, in influence games, can be considered centrality measures because an actor is more central in a network while more necessary is for generating of winning coalitions.

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