The order of criticality of a player in a simple game and two indices inspired by the reasoning à la Shapley and à la Banzhaf were introduced in two previous papers [3] and [4], respectively, mainly having in mind voting situations. Here, we devote our attention to graph connection games, and to the computation of the order of criticality of a player. The indices introduced in [4] may be used as centrality measures of the edges in preserving the connection of a graph.
Orders of Criticality in Graph Connection Games / Dall’Aglio, Marco; Fragnelli, Vito; Moretti, Stefano. - 11890:(2019), pp. 35-46. [10.1007/978-3-662-60555-4_3]
Orders of Criticality in Graph Connection Games
Dall’Aglio, MarcoWriting – Original Draft Preparation
;
2019
Abstract
The order of criticality of a player in a simple game and two indices inspired by the reasoning à la Shapley and à la Banzhaf were introduced in two previous papers [3] and [4], respectively, mainly having in mind voting situations. Here, we devote our attention to graph connection games, and to the computation of the order of criticality of a player. The indices introduced in [4] may be used as centrality measures of the edges in preserving the connection of a graph.
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