The Cohesiveness of Blocks In Social Networks: Node Connectivity and Conditional Density

Abstract

Abstract. The social cohesion of a group, as measured by patterns of network ties, increases with the level of redundancy of interconnections of its members. We will see that the minimal number k of independent paths that connect every pair of actors in a group, the higher the cohesion. The cohesiveness of a group is also measured by the extent to which it is not disconnected by removal of 1, 2, 3,..., n actors. Menger’s Theorem proves that these two measures are equivalent. Within this conceptual framework, we evaluate the family of concepts of cohesion and establish the validity of a pair of related measures: Connectivity – the minimum number k of its actors whose removal would not allow the group to remain connected or would reduce the group to but a single member – measures the social cohesion of a group at a general level; Conditional Density measures cohesion on a finer scale, that of surplus density beyond that implied by connectivity. For each k, these two measures may be combined into an aggregate measure of social cohesion, suitable for both small- and large-scale network studies. Using these measures within a new methodology of cohesive blocking we test hypotheses about the consequences of cohesion for social groups and their members, and demonstrate with empirical examples the significance and theoretical relevance of network cohesion as measured by connectivity in a variety of substantively important applications in sociology.