Katz centrality with an explicit baseline weight

The scaled resolvent form: beta = 1 recovers the plain Katz index and beta rescales every score linearly.

Usage

Katzcn(G, alpha = 0.1, beta = 1)

Arguments

G

Square adjacency matrix of the graph.

alpha

Positive attenuation factor.

beta

Baseline weight.

Value

List with estimate, centrality, alpha, beta, n, method.

Details

Formula: C_K = (I - alpha A)^{-1} beta 1.

References

Katz (1953), Psychometrika 18(1):39-43. doi:10.1007/BF02289026

Examples

Katzcn(matrix(c(0, 1, 1, 0, 0, 1, 1, 0, 0), 3, 3, byrow = TRUE))
#> $estimate
#> [1] 1.223458
#> 
#> $centrality
#> [1] 1.223458 1.112235 1.122346
#> 
#> $alpha
#> [1] 0.1
#> 
#> $beta
#> [1] 1
#> 
#> $n
#> [1] 3
#> 
#> $method
#> [1] "C_K = (I - alpha A)^{-1} beta 1, Katz (1953)"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"