Cliques and groups

Introduction: Groups and Sub-structures

• Most populations are more-or-less divided into sub-structures
• This creates structural holes and structural advantages
• Where an individual is located relative to sub-structures affects opportunities and constraints
• How the whole population is sub-structured affects diffusion, conflict, cohesion etc.

Bottom-up approaches: types of dyads, types of triads, the maximal complete sub-graph

• Cliques - maximal complete sub-graphs, clique overlap
• N-cliques - ties to all at distance LTE N
• N-clans - ties at distance N, but all ties within the clan
• K-plexes - direct ties to all but K others in the "plex"
• K-cores - direct ties to K others in the core
• F-group - valued data, transitive triads; strong = max value; weak = greater than a cutoff

Top-down approaches: strictly segregated sub-populations, degree of division, key positions and relations

• Components - disconnected sub-graphs
• Blocks and Cut-Points - "Bi-components" - connecting nodes
• Lambda Sets and Bridges - connecting relations
• Factions - "block model" of all within and no between ties

Summary: micro position, identity, and life chances; division and macro dynamics

Review Questions

1. Can you explain the term "maximal complete sub-graph?"

2. How do N-cliques and N-clans "relax" the definition of a clique?

3. Give an example of when it might be more useful to use a N-clique or N-clan approach instead of a strict clique.

4. How do K-plexes and K-cores "relax" the definition of a clique?

5. Give and example of when it might be more useful to us a K-plex or K-core approach instead of a strict clique.

6. What is a component of a graph?

7. How does the idea of a "block" relax the strict definition of a component?

8. Are there any cut points in the "star" network? in the "line" network? in the "circle" network?

9. How does the idea of a lambda set relax the strict definition of a component?

10. Are there any "bridges" in a strict hierarchy network?

Application Questions

1. Think of the readings from the first part of the course. Which studies used the ideas of group sub-structures? What kinds of approaches were used: cliques, clans, plexes, etc.?

2. Try to apply the notion of group sub-structures at different levels of analysis. Are there sub-structures within the kinship group of which you are a part? How is the population of Riverside divided into sub-structures? Are there sub-structures in the population of Universities in the United States? Are the nations in the world system divided into sub-structures in some way?

3. How might the lives of persons who are "cut points" be affected by having this kind of a structural position? Can you think of an example?

4. Can you think of a real-world (or literary) example of a population with sub-structures? How might the sub-structures in your real world case be described using the formal concepts (are the sub structures "clans" or "factions" etc.).