Questions: Network Centrality Measures and Node Importance

Question 1

Public health officials want to prioritize vaccination to most efficiently slow the spread of a contagious disease through a social contact network. Which centrality measure should guide their prioritization?

• A. Eigenvector centrality — targeting those connected to important people disrupts elite transmission chains
• B. Closeness centrality — vaccinating those who can reach everyone quickly prevents rapid spread
• C. Degree centrality — vaccinating the most-connected individuals removes the nodes with the most transmission routes
• D. Betweenness centrality — vaccinating bridges between communities is always the most efficient strategy

Answer: (C)

For disease spread, degree centrality (number of contacts) is the primary predictor of exposure risk and transmission potential — each contact is an independent transmission route. Degree centrality is the right lens because the question is about direct exposure, not about information gatekeeping or elite influence. Betweenness centrality becomes more relevant for inter-community spread (like halting a disease that has reached one cluster from reaching others), but degree is the foundational answer for individual transmission risk.

Question 2

Node X has 15 connections, all within a single densely connected clique. Node Y has 5 connections but serves as the only link between three otherwise disconnected communities. Which statement best describes their centrality profiles?

• A. Node X is more important by every measure because it has more connections
• B. Node Y has higher betweenness centrality despite lower degree centrality
• C. Node Y has both higher betweenness and higher eigenvector centrality than X
• D. Neither node is strategically important unless both are high on all centrality measures

Answer: (B)

Betweenness centrality measures how often a node lies on shortest paths between other pairs — Node Y, spanning three disconnected communities, sits on virtually every cross-community path and thus has extremely high betweenness. Node X, though highly connected, sits within a clique where every member can reach every other without passing through X. This demonstrates that degree and betweenness measure different things: local activity versus structural bridging. Eigenvector centrality depends on the centrality of Y's neighbors, not addressed here.

Question 3

A node with the highest degree centrality in a network will necessarily also have the highest betweenness centrality.

• T. True
• F. False

Answer: False

Degree and betweenness measure fundamentally different structural properties. A highly connected hub within a dense, isolated cluster can have low betweenness because all its connections stay within that cluster — other node pairs can reach each other without routing through it. Conversely, a modestly connected node that bridges otherwise disconnected communities can have very high betweenness with low degree. Knowing one centrality value tells you very little about a node's score on other measures.

Question 4

Eigenvector centrality scores a node higher if it is connected to other high-centrality nodes, meaning a single connection to a very central node can outweigh many connections to peripheral nodes.

• T. True
• F. False

Answer: True

Eigenvector centrality is recursive — your score depends on your neighbors' scores, which depend on their neighbors' scores, and so on. This is the logic behind Google's PageRank: a page linked by many prestigious pages scores higher than one linked by many obscure pages. In social networks, this captures prestige and embeddedness in influential clusters, which degree centrality misses entirely.

Question 5

Why does the choice of centrality measure constitute a substantive research decision rather than a purely technical one?

Model answer: Each centrality measure embeds a different theory of what 'importance' means in a network — degree assumes importance = number of contacts, betweenness assumes importance = control over flows between groups, eigenvector assumes importance = connection to other important actors. The right measure depends on what is flowing through the network and what question you are asking. Choosing the wrong measure can lead to identifying the wrong actors as key targets for intervention.

For disease transmission, high-degree nodes are the targets. For understanding information gatekeeping and who can suppress or distort rumors, betweenness identifies the brokers. For understanding elite influence and social capital, eigenvector identifies the core. The network structure is identical in all cases — the centrality measure is the analytical lens you apply based on your theoretical assumptions about how influence or spread operates.