The Strength of Indirect Relations in Social Networks

Here, our goal is to develop a formal analysis of dual network structures taking into account transitive completions of higher order than the usually considered triadic closure, i.e., allowing quadruple closure and any other higher order transitive completion of open n-paths traversing two dual social networks. In this way, a sequence of indirect relations might be generated in each social network, right next to the inherent direct relations in these networks. For this purpose, we introduce the setting of a “dual social network system” and we discuss how this setting might be produced in empirical situations, in which social networks are composed or partitioned in terms of various forms of actors’ categorizations from an attributional, attitudinal, typological or structural point of view. Furthermore, we are concerned with the issue of adjusting the concepts of Granovetter’s thesis on the strength of the weak ties to the case of direct and (any order) indirect relations in such dual social network systems.