ESM Network Analysis — Centrality Measures

Project Team Knowledge Network

A five-member project team shares the following undirected expertise-sharing ties:

A–B, A–C, A–D, B–C, D–E

where A = Alice, B = Bob, C = Carol, D = Dave, E = Eve.

Formulas:

Normalised degree centrality: $DC(v) = \deg(v) / (n-1)$

Network density: $\text{density} = |E| / \binom{n}{2}$

Normalised betweenness centrality:

$BC(v) = \frac{\displaystyle\sum_{s \neq v \neq t} \sigma_{st}(v) / \sigma_{st}}{(n-1)(n-2)/2}$

where $\sigma_{st}$ = total number of shortest paths from $s$ to $t$, and $\sigma_{st}(v)$ = those that pass through $v$.

Task 1: What is Alice's normalised degree centrality DC(A) in this five-person network?

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Task 2: What is the network density — the proportion of all possible ties that are present?

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Task 3: What is Alice's normalised betweenness centrality BC(A)?

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