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Mathematics LibreTexts

11.E: Cliques and Sub-groups (Exercises)

 

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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 an 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 an example of when it might be more useful to use 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 cutpoints 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 "cutpoints" 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.).