van den Brink, J.R., Borm, P., Hendrickx, R. and Owen, G. (2008). Characterizations of the Beta and the Degree Network Power Measure Theory and Decision, 64:519--536.

A symmetric network consists of a set of positions and a set of bilateral links between these positions. 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 be proportional to 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. {\textcopyright} 2007 Springer Science+Business Media LLC.