Orders of Criticality in Graph Connection Games

The order of criticality of a player in a simple game and two indices inspired by the reasoning \ue0 la Shapley and \ue0 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

Lecture Notes in Computer Science book series (LNCS, volume 11890)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