Liberté, Égalité, Fraternité – a power study in signed networks –

Power in human societies is a central phenomenon. Even though, it took ages to understand it and - even more - to measure it. Only in the last decades attempts were made to model power relations and to assign respective power indices to actors in a network. The present work goes a step further. It measures power of actors and groups of actors in signed networks consisting of positive and negative relations. In a probabilistic framework, such relations are specified as conditionals: Which actor receives power given that the adjacent actor has it, and which actor looses power given that the neighbour dominates. This pattern of power relations allows for an exact calculation of an actor's and groups of actors' power index. The new theory is applied to a middle size Kronecker net of clans and subclans operating in a today's society