Eigenvector centrality

Formula: A x = lambda_max x; centrality is the principal eigenvector

Usage

Eigcent(A)

Arguments

A

See Usage.

Value

List with centrality (max-scaled), unit, eigenvalue, n.

References

Bonacich (1972), Factoring and weighting approaches to status scores and clique identification, Journal of Mathematical Sociology 2:113-120. Paywalled; the measure is the principal eigenvector of the adjacency matrix, as it is universally described in the centrality literature (e.g. Bonacich 2000, Social Networks 22:357-365, which restates his own definition).

Examples

Eigcent(matrix(c(0, 1, 1, 1, 0, 1, 1, 1, 0), 3, 3))
#> $centrality
#> [1] 1 1 1
#> 
#> $unit
#> [1] 0.5773503 0.5773503 0.5773503
#> 
#> $eigenvalue
#> [1] 2
#> 
#> $n
#> [1] 3
#> 
#> $method
#> [1] "Eigenvector centrality (principal eigenvector)"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"