Structures of connectivity

From the earliest days of research on blockmodeling, one primary goal was to develop a method that would exploit the algebra of the social relations among individuals to describe the social structure of the group. This goal was reluctantly abandoned, however, because the presence of idiosyncratic relational ties in the data obscured the structure and no reliable method for identifying these ties existed. This paper presents such a method. We have found it useful to distinguish emotionally weak ties (Granovetter 1973), those with low intensity, from structurally weak ties, those that fail to conform to the pattern of ties that exist in and are reinforced by the social structure. The latter type of weak ties are the idiosyncratic ties that interfere with attempts to describe a social structure. This paper operationalizes the concept of structurally weak ties and presents an algebraic method for identifying them in sociometric data. This enables us to use the algebra of social relations to identify a blockmodel that describes the social structure of the group.