Network analysis glossary
Closeness centrality
Closeness centrality measures how near a person is to everyone else in the network, counted in steps along ties. A person with high closeness can reach the whole group quickly, which makes them well placed to spread news or notice what is happening anywhere in the network.
Updated · Netgraf
| Person | Harmonic closeness |
|---|---|
| Diane | 0.787 |
| Fernando | 0.759 |
| Garth | 0.759 |
| Andre | 0.676 |
| Beverly | 0.676 |
Harmonic closeness, 0 to 1: the average of 1 / distance to everyone else. Computed live from the example map with the same code the Netgraf insights panel runs.
How it's calculated
classic closeness(v) = (n - 1) / sum of distance(v, u) over all u harmonic closeness(v) = (1 / (n - 1)) * sum of 1 / distance(v, u) over all u
The classic form breaks the moment a network has two separate islands, because the distance to an unreachable person is infinite. Harmonic closeness, proposed by Marchiori and Latora in 2000, sums 1 / distance instead, so an unreachable person simply adds 0. Netgraf uses the harmonic form because real relationship maps very often have islands in them.
The kite, and why the measures disagree
Krackhardt drew his kite so that three people would each be "most central" by a different measure: Diane by degree, Heather by betweenness, and Fernando and Garth by classic closeness, since they have the shortest total distance to everyone. Harmonic closeness rewards many one-step ties more heavily, so on the kite it puts Diane narrowly ahead of Fernando and Garth. The live figures below show how close it is. Neither is wrong; they weigh near and far contacts differently.
In Netgraf
Closeness is exported for every person in the People CSV and in GraphML, next to degree, betweenness, PageRank (as influence) and clustering. The Insights panel's Steps apart figure is the related average: the mean shortest path between any two people in the largest connected group.