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Mathematics LibreTexts

10.E: Centrality and Power (Exercises)

  • Page ID
    7712
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    Review Questions

    1. What is the difference between "centrality" and "centralization"?
    2. Why is an actor who has higher degree a more "central" actor?
    3. How does Bonacich's influence measure extend the idea of degree centrality?
    4. Can you explain why an actor who has the smallest sum of geodesic distances to all other actors is said to be the most "central" actor, using the "closeness" approach?
    5. How does the "flow" approach extend the idea of "closeness" as an approach to centrality?
    6. What does it mean to say that an actor lies "between" two other actors? Why does betweenness give an actor power or influence?
    7. How does the "flow" approach extend the idea of "betweenness" as an approach to centrality?
    8. Most approaches suggest that centrality confers power and influence. Bonacich suggests that power and influence are not the same thing. What is Bonacich's argument? How does Bonacich measure the power of an actor?

    Application Questions

    1. Think of the readings from the first part of the course. Which studies used the ideas of structural advantage, centrality, power, and influence? What kind of approach did each use: degree, closeness, or betweenness?
    2. Can you think of any circumstances where being "central" might make one less influential? Less powerful?
    3. Consider a directed network that describes a hierarchical bureaucracy, where the relationship is "gives orders to". Which actors have highest degree? Are they the most powerful and influential? Which actors have high closeness? Which actors have high betweenness?
    4. Can you think of a real-world example of an actor who might be powerful but not central? Who might be central, but not powerful?