Characterizations of Network Power Measures
van den Brink, René
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A symmetric network consists of a set of positions and a set of bilateral links between these positions. Examples of such networks are exchange networks, communication networks, disease transmission networks, control networks etc. For every symmetric network we define a cooperative transferable utility game that measures the “power” of each coalition of positions in the network. Applying the Shapley value to this game yields a network power measure, the β-measure, which reflects the power of the individual positions in the network. Applying this power distribution method iteratively yields a limit distribution, which turns out to equal the well-known degree measure. We compare the β- measure and degree measure by providing characterizations, which differ only in the normalization that is used.
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