Eigenvector Centrality

Eigenvector centrality (Bonacich 1972) scores a node by the scores of the nodes that point to it. The scores form the dominant eigenvector of the transposed weight matrix: $$\lambda x = A^{T} x.$$ The vector is scaled to a maximum of one.

Usage

centrality_eigenvector(x, ...)

Arguments

x

Network input accepted by centrality.

...

Further arguments to centrality, such as directed.

Value

A named numeric vector with one score per node, in input node order.

Details

\(A\) holds the edge weights, or ones with weighted = FALSE. On a directed network a node gains standing from its incoming edges. The scores lie between 0 and 1. A network without edges gives every node a score of one.

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 .

See also

centrality_pagerank, centrality_alpha, centrality_authority, centrality.

Examples

centrality_eigenvector(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>  0.7209674  0.2010163  1.0000000  0.8380103  0.7619198  0.5077694  0.1980065 
#>   Evaluate     Create      Share 
#>  0.4995074  0.6689427  0.5849834