Structural cohesion is the sociological and graph theory conception ^[1][2] and measurement of cohesion for maximal social group or graphical boundaries where related elements cannot be disconnected except by removal of a certain minimal number of other nodes. The solution to the boundary problem for structural cohesion is found by the vertex-cut version of Menger's theorem. The boundaries of structural endogamy are a special case of structural cohesion. 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. A pictorial representation of a graph In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. ... Cohesion may mean: Cohesion (chemistry): the intermolecular attraction between like-molecules. ... In sociology, a group is usually defined as a collection consisting of a number of people who share certain aspects, interact with one another, accept rights and obligations as members of the group and share a common identity. ... In the mathematical discipline of graph theory and related areas, Mengers theorem is a basic result about connectivity in finite undirected graphs. ... K-cores in graph theory were introduced by V. Batagelj, M. Zaversnik in the article Generalized Cores. ...

Examples

Some illustrative examples are presented in the gallery below:

The 6-node ring in the graph has connectivity-2 or a level 2 of structural cohesion because the removal of two nodes is needed to disconnect it. Image File history File links NetworkTopology-Ring. ...

The 6-node component (1-connected) has an embedded 2-component, nodes 1-5 Image File history File links 6n-graf. ...

A 6-node clique is a 5-component, structural cohesion 5

See also

• Social network
• Social-circles network model

// An example of a social network diagram Social network analysis views social relationships in terms of nodes and ties. ... The generative model of feedback networks studied in mathematics and physics by White, Kejžar, Tsallis, Farmer, and White, or social-circles network model, defines a class of random graphs generated by simple processes that are common to edge formation and feedback loops in social circles. ...

References

1. ^ Moody, James; White, Douglas (2003). "Structural Cohesion and Embeddedness: A Hierarchical Concept of Social Groups." (PDF). American Sociological Review 68 (1): 1-25. Retrieved on 2006-08-19. 
2. ^ White, Douglas; Frank Harary (2001). "The Cohesiveness of Blocks in Social Networks: Node Connectivity and Conditional Density." (book). Sociological Methodology 2001 31 (1): 305-359. Retrieved on 2006-08-19.