Katz centrality excluding the length-zero walk

The variant that drops the k = 0 term of the resolvent series, so a node with no incident walks scores zero instead of one. The additive constant beta shifts every score equally.

Usage

Katzc(y, A, alpha = 0.1, beta = 0)

Arguments

y

Node weights applied to the seed vector; ones give Katz's own definition.

A

Square adjacency matrix.

alpha

Positive attenuation factor.

beta

Additive constant.

Value

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

Details

Formula: x = (I - alpha A)^{-1} (alpha A) y + beta.

References

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

Examples

Katzc(y = c(1, 1, 1), A = matrix(c(0, 1, 1, 0, 0, 1, 1, 0, 0), 3, 3, byrow = TRUE))
#> $estimate
#> [1] 0.223458
#> 
#> $centrality
#> [1] 0.2234580 0.1122346 0.1223458
#> 
#> $alpha
#> [1] 0.1
#> 
#> $beta
#> [1] 0
#> 
#> $n
#> [1] 3
#> 
#> $method
#> [1] "x = (I - alpha A)^{-1} (alpha A) y + beta, Katz (1953)"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"