Chapter 20 Quiz: Six Degrees — How Small-World Networks Open Big Doors
15 questions. Read each question carefully before checking the answer.
Question 1. In Milgram's original small-world experiment, what was the approximate average length of completed chains?
A) 2–3 intermediaries B) 5.5–6 intermediaries C) 10–12 intermediaries D) 20–25 intermediaries
Show Answer
**B — 5.5 to 6 intermediaries.** Milgram's 1967–1969 experiments, in which participants tried to route a booklet to a target person in Boston through personal acquaintances, produced average chain lengths of approximately 5.5 to 6 intermediaries. This is the origin of the "six degrees of separation" phrase.Question 2. The Watts-Strogatz (1998) model identified two defining properties of a small-world network. Which answer correctly names both?
A) High degree centrality and low betweenness centrality B) High clustering coefficient and short average path length C) Power-law degree distribution and high transitivity D) Low clustering and long path length with random shortcuts
Show Answer
**B — High clustering coefficient and short average path length.** The Watts-Strogatz definition of a small-world network requires (1) high clustering — the tendency of connected nodes to share neighbors (my friends' friends tend to be my friends) — and (2) short average path length — despite the clustering, any two nodes are surprisingly few hops apart. The model showed these co-occur when a small fraction of edges are randomly rewired as long-range connections.Question 3. In the Watts-Strogatz model, what happens to average path length when even a small fraction of edges in a regular lattice are randomly "rewired" to connect distant nodes?
A) Average path length increases substantially, because random connections disrupt the lattice structure B) Average path length decreases dramatically, while clustering changes very little C) Both average path length and clustering decrease proportionally D) Average path length decreases slightly, but only after a majority of edges are rewired
Show Answer
**B — Average path length decreases dramatically, while clustering changes very little.** This is the key mathematical finding of the Watts-Strogatz paper. A small number of random long-range "shortcuts" is sufficient to dramatically reduce average path length — turning a large, regular lattice into a small-world network — while the high local clustering (friends of friends are friends) is barely affected, because it is maintained by the many local edges that remain.Question 4. What is a "hub" in network science, and why are hubs essential to small-world dynamics?
A) A hub is a node with zero connections, which creates space for new edges; its absence reduces path length by removing detours B) A hub is a highly connected node that acts as a super-shortcut — connecting to it connects you, in effect, to everyone it connects to, dramatically reducing average path length C) A hub is any node with exactly the network-average number of connections; hubs are essential because they define the network's mean D) A hub is a node that bridges exactly two otherwise disconnected components; essential because it provides the only path between them
Show Answer
**B — A hub is a highly connected node that acts as a super-shortcut — connecting to it connects you, in effect, to everyone it connects to, dramatically reducing average path length.** Hubs are nodes with far more connections than average. In networks with power-law degree distributions (most real-world social networks), a small number of hubs have vastly more connections than average nodes. These hubs serve as shortcuts: routing a message through a hub can traverse what would otherwise be many intermediate steps in a single hop.Question 5. Barabási and Albert's "preferential attachment" model predicts that network connectivity will follow which distribution?
A) A normal (bell-curve) distribution, with most nodes near average connectivity B) A uniform distribution, with equal numbers of nodes at each connectivity level C) A power-law distribution, where most nodes have few connections and a small number have many D) An exponential distribution, where connectivity decays rapidly from a maximum value
Show Answer
**C — A power-law distribution, where most nodes have few connections and a small number have many.** Preferential attachment — new nodes connecting preferentially to already well-connected nodes — naturally produces power-law distributions. This "rich get richer" dynamic in networks explains why real-world social networks have hubs: nodes that joined early and attracted connections disproportionately continue to attract more connections over time.Question 6. The Microsoft Messenger study (Leskovec and Horvitz, 2008) analyzed 240 million users and found what average path length?
A) 3.2 hops B) 4.8 hops C) 6.6 hops D) 9.1 hops
Show Answer
**C — 6.6 hops.** The Microsoft Research study analyzing 30 billion messages across 240 million Messenger users found an average path length of 6.6 hops — remarkably close to Milgram's six degrees finding from nearly four decades earlier, achieved through a fundamentally different method on an incomparably larger and more representative dataset.Question 7. The Microsoft Messenger study also found that approximately what fraction of user pairs had NO path between them?
A) Less than 5% B) Approximately 15% C) Approximately 30% D) Approximately 48%
Show Answer
**D — Approximately 48%.** The study found that roughly 48% of user pairs in the network were in disconnected components — with no path between them at all. "Six degrees" applies only to the connected portion of any network. This is an important qualification: the short average path length applies to pairs who are reachable to each other, not to all possible pairs globally.Question 8. Gladwell's concept of "Connectors" in The Tipping Point has been criticized by network scientists on which grounds?
A) Connectors don't actually exist — network connectivity follows a normal distribution with no outliers B) Apparent super-connectors may be early network joiners who accumulated connections through preferential attachment rather than through a special personality trait; and hub status is domain-specific C) Connectors are too socially powerful — Gladwell's framework gives them too little credit for their structural role D) Connectors uniformly create opportunity for all their contacts — the research shows no difference in how they treat different types of connections
Show Answer
**B — Apparent super-connectors may be early network joiners who accumulated connections through preferential attachment rather than through a special personality trait; and hub status is domain-specific.** The chapter presents two key critiques of Gladwell's Connector concept: (1) many apparent connectors are not uniquely gifted but are simply early joiners who accumulated connections through the standard preferential attachment mechanism, and (2) hub status is domain-specific — a connector in the art world may have zero bridging function in technology. Gladwell's treatment arguably overstates the personality-as-cause and understates the structural explanation.Question 9. The chapter says topological path length and navigational path length are different. What is the distinction?
A) Topological path length measures geographic distance; navigational path length measures social distance B) Topological path length is the shortest path that exists in the network structure; navigational path length is the path that can actually be found by asking people to route toward a target C) Topological path length counts all intermediaries; navigational path length counts only those who actively participate D) Topological path length is measured in social network analysis software; navigational path length is self-reported by research participants
Show Answer
**B — Topological path length is the shortest path that exists in the network structure; navigational path length is the path that can actually be found by asking people to route toward a target.** The distinction matters because short paths exist in many networks that people cannot easily find without knowing the network structure. Milgram's experiment measured navigational success, showing that people can route reasonably efficiently through social networks even without seeing the full map. LinkedIn's mutual connection display makes topological paths visible, substantially improving navigability.Question 10. In the Kevin Bacon game, the average Bacon number for actors in the database is approximately:
A) 1.2 B) 2.9 C) 5.1 D) 7.3
Show Answer
**B — Approximately 2.9.** The average Bacon number in the Hollywood collaboration network is approximately 2.9 — fewer than three steps. This reflects the small-world structure of the Hollywood network, which has high clustering (actors who work together tend to work with each other's frequent collaborators) and multiple hubs (prolific actors who have worked across many films and genres, providing shortcuts across the network).Question 11. The chapter describes three mechanisms through which social media has collapsed degrees of separation. Which of the following is NOT one of those mechanisms?
A) Transparency of connections (making network structure visible) B) Asymmetric reach (allowing communication to people outside your direct network) C) Content amplification (a single post can reach thousands through sharing) D) Algorithmic enforcement of strong ties (prioritizing close connections in feeds)
Show Answer
**D — Algorithmic enforcement of strong ties (prioritizing close connections in feeds).** The chapter identifies three mechanisms through which social media collapses degrees of separation: (1) transparency of connections (LinkedIn's mutual connection display), (2) asymmetric reach (Twitter/X, Instagram, LinkedIn allowing communication to non-connected accounts), and (3) communication amplification (posts reaching thousands through sharing). Algorithmic prioritization of strong ties — if anything — works against this collapse by concentrating attention on already-connected people.Question 12. According to Kleinberg's navigability research, for a small-world network to be efficiently navigable (not just topologically short), the distribution of long-range connections must:
A) Follow a uniform distribution across all distances B) Follow a specific pattern where the probability of connection decreases with distance at a particular rate C) Be concentrated among hub nodes only D) Include at least one direct connection from every node to a hub
Show Answer
**B — Follow a specific pattern where the probability of connection decreasing with distance at a particular rate.** Kleinberg's theoretical result showed that not all small-world networks are navigable. Efficient navigation (where decentralized routing strategies can find short paths) requires the long-range connection probability to decrease with distance according to a specific power law. If the decay is too fast or too slow, navigation fails even when short paths exist topologically.Question 13. The chapter's Python code uses the NetworkX library to calculate the shortest path between two nodes. What does the "shortest path" represent in the context of Priya's network?
A) The path between nodes that requires the fewest total relationship-maintenance hours B) The sequence of people connecting Priya to Daniel Osei with the fewest intermediate connections C) The path that passes through the most highly connected intermediate nodes D) The connection chain with the strongest average tie strength
Show Answer
**B — The sequence of people connecting Priya to Daniel Osei with the fewest intermediate connections.** In graph theory, the shortest path between two nodes is the path with the fewest edges (hops). In the context of Priya's social network, this translates to the chain of people connecting her to her target with the fewest intermediate handshakes. NetworkX's `shortest_path` function finds this chain computationally.Question 14. The hub strategy for network building suggests that connecting to hub nodes is more valuable than connecting to regular nodes. Why?
A) Hubs have more resources to share directly, including job offers and financial capital B) Hubs are more trustworthy because their large network has vetted them repeatedly C) Connecting to a hub expands your two-hop reachable network by the hub's full connection count, multiplying your reach far more than connecting to average nodes D) Hubs have longer tenure in the network, giving them access to more historical information
Show Answer
**C — Connecting to a hub expands your two-hop reachable network by the hub's full connection count, multiplying your reach far more than connecting to average nodes.** The strategic value of connecting to a hub is multiplicative: if a hub has 500 diverse connections, your two-hop reachable network expands by approximately 500 in a single step. A connection to a regular node with 20 connections expands your reach by 20. Since weak tie value comes from bridging to new information environments, and hubs bridge to more environments, the return on investment in hub relationships is disproportionately high.Question 15. Priya had been cold-applying through a job portal for six weeks before discovering she was two hops from the hiring manager. The chapter's main lesson from this story is:
A) Job portals are ineffective and should be abandoned in favor of exclusive networking events B) Understanding small-world network structure enables people to find and traverse chains that were always present but invisible — changing "cold-applying" into "chain-connecting" C) LinkedIn is more reliable than job portals because it screens for candidate quality before surfacing applications D) The only way to find a job is through direct personal connections to hiring managers