Weighted interaction semigroups

Current semigroup models of social systems assume that the system is unifor m, that is all the units and all the connections in the system have the sam e influence. Obviously most social structures are not uniform; some units a nd connections between some units are more influential and important than s ome others. This paper initiates a development of the semigroup model of so cial structures that reflects this non-uniformity by using weighted inner p roducts in generation of interaction semigroups.