Power, centrality, and hierarchy

Today’s Dad Joke

Bro, can you pass me that leaflet?

Brochure.

What is power?

Long, varied history in the social sciences
- One version is the capacity to achieve one’s will
- How do we do that? Through capital
Social networks are one way of measuring “social capital”
Who has power in a social network?

Degree Centrality

Counts the number of edges each node has
In, out, or all

[1] "Degree Centrality:"

 1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 
16  9 10  6  3  4  4  4  5  2  3  1  2  5  2  2  2  2  2  3  2  2  2  5  3  3 
27 28 29 30 31 32 33 34 
 2  4  3  4  4  6 12 17

Closeness Centrality

Average distance to all other nodes

Betweenness Centrality

Counts the number of shortest paths that go through each node. This is based on the value of being in a “structural hole”

Which of these has the highest betweenness?

Eigenvector Centrality

It’s not what you know, it’s who you know

Network-level

Density

Directed \[ \frac{\sum(edges)}{N * (N-1)} \]

Undirected: Multiply by 2

Centralization

How unequal is the centrality between nodes?

Betweenness Centralization scores:

[1] 0.1972789

[1] 1

[1] 0

Hierarchy

Does information flow from the top down or in both directions?

[1] "Hierarchy of advice network:"

      Mut 
0.4761905