The cohesiveness of blocks in social networks: Node connectivity and conditional density

This study shows several ways that formal graph theoretic statements map patterns of network ties into substantive hypotheses about social cohesion. If network cohesion is enhanced by multiple connections between members of a group, for example, then the higher the global minimum of the number of independent paths that connect every pair of nodes in the network, the higher the social cohesion. The cohesiveness of a group is also measured by the extent to which it is not disconnected by removal of 1, 2, 3,..., k actors. Menger's Theorem proves that these two measures are equivalent. Within this graph theoretic framework, we evaluate various concepts of cohesion and establish the validity of a pair of related measures: 1. 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. 2. Conditional density measures cohesion on a finer scale as a proportion of ties beyond that required for connectivity k over the number of ties that would force it to k + 1. Calibrated for successive values of k, these two measures combine into an aggregate measure of social cohesion, suitable for both small- and large-scale network studies. Using these measures to define the core of a new methodology of cohesive blocking, we offer hypotheses about the consequences of cohesive blocks for social groups and their members, and explore empirical examples that illustrate the significance, theoretical relevance, and predictiveness of cohesive blocking in a variety of substantively important applications in sociology.