ntevc

Eigenvector centrality of each node

R

ntevc(from, to, w = NULL, nodes = NULL, tol = 1e-13, maxit = 1e+05)

The leading eigenvector of the (weighted) adjacency matrix of the undirected graph, scaled to a maximum of 1 (Bonacich 1972). It is found by power iteration on A + c I, c the largest weight, which has the same eigenvectors and whose leading eigenvalue is strictly dominant even on a bipartite graph (a co-offending network between two roles, a star), where plain power iteration oscillates. The iteration starts from 1 for every node and stops when no value changes by tol or more between two steps, or after maxit steps (then conv is FALSE).

Parameters

from, to

Labels of the two ends of each edge: vectors of the same length (zero when nodes gives every node) with no missing values.

w

NULL, or one positive weight per edge (a tie’s strength, such as the number of co-offences).

nodes

NULL, or every node’s label once: the node order of the results and the way to include isolated nodes.

tol

The stopping tolerance: one number between 0 and 1.

maxit

The most steps: one whole number, at least 1.

Returns

A list: cent, a data frame with node and evc; value, the leading eigenvalue; iter, the steps taken; conv, whether the tolerance was met.

Notes

On a disconnected graph the leading eigenvector lives on the components with the largest leading eigenvalue; every other component gets 0 (each component is iterated and scaled on its own, and a component whose eigenvalue falls short of the largest by more than 1e-10 of it is set to 0). When several components share the largest eigenvalue each is scaled to a maximum of 1: any mix of them is an eigenvector too, so compare nodes within a component. A graph without edges gives 1 for every node. Graph rules as in ntdeg().

References

Bonacich, P. (1972). Factoring and weighting approaches to status scores and clique identification. Journal of Mathematical Sociology, 2(1), 113-120. doi:10.1080/0022250X.1972.9989806

Examples

ntevc(c("hub", "hub", "hub", "a"), c("a", "b", "c", "b"))

Generated from the R help page: ntevc in the R reference.