||This article may be too technical for most readers to understand. (November 2010)|
Structural cohesion is the sociological 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. 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.
Some illustrative examples are presented in the gallery below:
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.
- Moody, James; White, Douglas (2003). "Structural Cohesion and Embeddedness: A Hierarchical Concept of Social Groups." (PDF). American Sociological Review 68 (1): 1–25. Retrieved 2006-08-19.
- White, Douglas; Frank Harary (2001). "The Cohesiveness of Blocks in Social Networks: Node Connectivity and Conditional Density." (book). Sociological Methodology 2001 (Blackwell Publishers, Inc., Boston, USA and Oxford, UK.) 31 (1): 305–359. doi:10.1111/0081-1750.00098. Retrieved 2012-08-13.
- Chin, Wynne W., et al. Perceived Cohesion: A Conceptual and Empirical Examination: Adapting and Testing the Perceived Cohesion Scale in a Small-Group Setting. 1999. Small Group Research 30(6):751-766.