Lowest number of people removed to disconnect a social group
In sociology, structural cohesion is the conception of a useful formal definition and measure of cohesion in social groups. It is defined as the minimal number of actors in a social network that need to be removed to disconnect the group. It is thus identical to the question of the node connectivity of a given graph in discrete mathematics. The vertex-cut version of Menger's theorem also proves that the disconnection number is equivalent to a maximally sized group with a network in which every pair of persons has at least this number of separate paths between them. It is also useful to know that k-cohesive graphs (or k-components) are always a subgraph of a k-core, although a k-core is not always k-cohesive. A k-core is simply a subgraph in which all nodes have at least k neighbors but it need not even be connected. 
The boundaries of structural endogamy in a kinship group are a special case of structural cohesion.
Software.
Cohesive.blocking is the R program for computing structural cohesion according to the Moody-White (2003) algorithm. This wiki site provides numerous examples and a tutorial for use with R.
Examples.
Some illustrative examples are presented in the gallery below:
Perceived cohesion.
Perceived Cohesion Scale (PCS) is a six item scale that is used to measure structural cohesion in groups. In 1990, Bollen and Hoyle used the PCS and applied it to a study of large groups which were used to assess the psychometric qualities of their scale.
References.
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