Chapter 11 Exercises

Conceptual Review

Exercise 11.1 — Network Vocabulary Match each term to its correct definition by writing the letter in the blank.

Exercise 11.2 — Preferential Attachment In your own words (3–4 sentences), explain why preferential attachment produces scale-free networks. Your explanation should address: (a) what preferential attachment means in the context of a fan community; (b) why this process produces heavy-tailed degree distributions; and (c) one reason why the process might be considered unfair.

Exercise 11.3 — Community Formation Stages The table below describes four fan communities at different stages of formation. For each, identify the stage (nucleation, crystallization, consolidation, maturation) and explain your reasoning.

Analytical Exercises

Exercise 11.4 — Network Map Draw (by hand or using software) a rough network diagram of a fan community you know. Include at least 15 nodes. Label: - At least 2 hub nodes (explain why you classified them as hubs) - At least 1 bridge node (explain what communities it connects) - At least 3 peripheral/lurker nodes

After drawing the map, answer: What does your map reveal about the community that a survey of fan opinions would not?

Exercise 11.5 — Calculating Density A small fan Discord server has 50 members. During the previous month, 120 unique pairs of members interacted with each other (a pair is counted once even if they interacted multiple times).

(a) What is the maximum possible number of unique pairs in a 50-member network? (b) Calculate the network density. (c) If 10 new members join but none of them interact with existing members, what happens to density? Why? (d) If 10 new members join and each interacts with 5 existing members, recalculate the density.

Exercise 11.6 — Strong Ties, Weak Ties, and Information Flow Mireille's Manila ARMY server has 40,000 members. Her strong-tie network within the server (people she knows personally) is roughly 30 people. @armystats_global has 120,000 Twitter followers, the vast majority of whom it does not know personally.

(a) Which of these two accounts would you expect to hear first about a new BTS chart milestone? Explain using Granovetter's theory. (b) Which would be more effective at rapidly communicating that milestone to a global ARMY audience? Explain. (c) What does this suggest about the respective roles of Mireille and @armystats_global in the ARMY network?

Exercise 11.7 — Structural Holes Priya Anand and IronHeartForever both occupy bridge positions in the Kalosverse network, but they bridge different structural holes.

(a) What two communities does Priya bridge? What is the nature of the gap between them? (b) What two communities does IronHeartForever bridge? What is the nature of that gap? (c) What information advantages does each broker have that the other does not? (d) What costs or risks does each broker face that a high-degree hub like KingdomKeeper_7 does not?

Applied Exercises

Exercise 11.8 — Running the Code Run fan_network_analysis.py from this chapter's code/ directory. After running it:

(a) What is the degree of the top hub node in your generated network? How does this compare to the average degree? (b) Calculate the ratio of top hub degree to average degree. What does this ratio tell you about inequality in the network? (c) Which simulation (random failure vs. targeted attack) produced a larger reduction in the largest connected component? Does this result match what you predicted from the chapter reading? Explain. (d) Modify the script to run with n_fans=2000 and m=5. How do the network statistics change? What does this suggest about how denser fan communities differ structurally from sparser ones?

Exercise 11.9 — Community Detection Analysis Run community_detection.py from this chapter's code/ directory.

(a) What modularity score did the algorithm achieve? How would you interpret this score? (b) How many communities did the algorithm detect? Does this match the number planted (5)? (c) For each detected community, what fan practice does it most closely correspond to? How did you determine this? (d) The Destiel community was planted as the largest community (120 fans). Was it also detected as a single community, or was it split? What might account for this?

Exercise 11.10 — Platform Migration Scenario Imagine that Discord permanently shuts down its servers (a deliberately extreme scenario). The ARMY Manila server Mireille manages has 40,000 members.

(a) Draw a rough diagram of which edges (connection types) in Mireille's network depend on Discord-specific features and which do not. (b) Which members of the community do you predict would follow a platform migration to an alternative? Which would not? (Think about the role of strong vs. weak ties.) (c) What network structural features would Mireille want to build in advance to maximize resilience to this kind of disruption? (d) Would a platform migration affect Mireille's node (her network position) more than it would affect KingdomKeeper_7's position in the Kalosverse? Why or why not?

Discussion Questions

11.D1 KingdomKeeper_7 became a hub partly through being active during the Kalosverse's crystallization stage. Does this make his authority in the community less legitimate? What is the relationship between structural position and legitimacy?

11.D2 If fan communities' network structure is partly determined by mathematical processes (preferential attachment), what does this imply for fans who want to build more egalitarian communities? Is structural equality possible? What would it require?

11.D3 @armystats_global operates primarily through weak ties. What does this suggest about what it means to be a "community member"? Can someone who has only weak ties to a community be meaningfully part of it?

11.D4 The Tumblr 2018 ban disproportionately affected communities that had concentrated their activity on a single platform. Is it fair to say those communities "should have known better" and distributed their activity? What would this critique assume about the resources and knowledge available to fan community organizers?