Network analysis glossary
Eigenvector centrality and PageRank
Eigenvector centrality scores a person by the importance of the people they are tied to, not just by how many ties they have. A tie to a well-connected person counts for more than a tie to someone on the edge. PageRank, the measure behind Google's original search ranking, is a variant that stays well defined on any network.
Updated · Netgraf
| Person | PageRank |
|---|---|
| John A. | 10.1% |
| Mr. Hi | 9.7% |
| Member 33 | 7.2% |
| Member 3 | 5.7% |
| Member 2 | 5.3% |
PageRank with damping 0.85. The scores sum to 100% across the map. Computed live from the example map with the same code the Netgraf insights panel runs.
How it's calculated
eigenvector: x(v) = (1 / lambda) * sum of x(u) over neighbours u of v PageRank: r(v) = (1 - d) / n + d * sum of r(u) / degree(u) over neighbours u
Phillip Bonacich formalised eigenvector centrality for social networks in 1972 and generalised it in 1987. PageRank adds two things: each person splits their score among their ties rather than giving it to each in full, and a small share (1 - d) is spread evenly across everyone. That second step is what keeps PageRank defined on networks with several separate groups, where eigenvector centrality collapses onto the largest group and scores everyone else zero.
What it tells you
Use it to find influence that runs through connections: the person who knows fewer people but knows the right ones. In Zachary's karate club the two leaders, the instructor Mr. Hi and the club officer John A., top every measure, but PageRank also lifts the members closest to them above others with the same number of ties.
In Netgraf
Netgraf computes PageRank rather than raw eigenvector centrality, for the reason above. In the Insights panel it is Widest reach: people "tied to people who are themselves well tied". Choose it to resize every dot by it.