Network analysis glossary
Betweenness centrality
Betweenness centrality measures how often a person lies on the shortest path between two other people. A person with high betweenness is a broker: information, money or influence moving between parts of the network tends to pass through them, and removing them makes everyone else further apart.
Updated · Netgraf
| Person | Betweenness |
|---|---|
| Medici | 0.522 |
| Guadagni | 0.255 |
| Albizzi | 0.212 |
| Salviati | 0.143 |
| Ridolfi | 0.114 |
Normalised to 0 to 1: the share of all shortest paths between other pairs that pass through each person. Computed live from the example map with the same code the Netgraf insights panel runs.
How it's calculated
betweenness(v) = sum over pairs s, t (s != v != t) of paths(s, t through v) / paths(s, t) normalised = betweenness(v) / ((n - 1)(n - 2) / 2)
Linton Freeman defined the measure in 1977. Computing it naively takes a very long time on large networks; Ulrik Brandes's 2001 algorithm, which Netgraf uses, does it with one breadth-first search from every person.
The Medici
The best-known result in the field comes from the Florentine families. Padgett and Ansell mapped the marriage and business ties of fifteenth-century Florence's elite and found that the Medici were neither the wealthiest family nor the most established politically. They were the family that sat between the others: many of the families they married into had no ties to each other. That brokerage position, not raw size, is what the Medici turned into power. Their betweenness is by far the highest on the map.
In Netgraf
In the Insights panel, betweenness is Holding it together: people who "sit between people who would otherwise be far apart". Choose it and the dots on the map are resized by betweenness, so the brokers stand out. Related: brokers and cut points, the people whose removal would actually split the map.