HITS Authority and Hub Scores

The HITS algorithm (Kleinberg 1999) assigns each node an authority score from the hubs that point to it and a hub score from the authorities it points to: $$a = \lambda^{-1} A^{T} h, \qquad h = \lambda^{-1} A a .$$ Authorities are the dominant eigenvector of \(A^{T} A\) and hubs the dominant eigenvector of \(A A^{T}\).

Usage

centrality_authority(x, ...)

centrality_hub(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. Both scores are scaled to a maximum of one, so they lie between 0 and 1. On an undirected network both equal eigenvector centrality. A network without edges gives every node a score of one. centrality_hub() returns the hub scores.

References

Kleinberg, J. M. (1999). Authoritative sources in a hyperlinked environment. Journal of the ACM, 46(5), 604-632. doi:10.1145/324133.324140 .

See also

centrality_eigenvector, centrality_pagerank, centrality.

Examples

centrality_authority(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#> 0.30736489 0.21141184 1.00000000 0.67930404 0.40566475 0.62132791 0.05601863 
#>   Evaluate     Create      Share 
#> 0.93786061 0.40032707 0.74285635 
centrality_hub(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>  0.2889344  1.0000000  0.2166116  0.2588081  0.1394834  0.2448074  0.2223682 
#>   Evaluate     Create      Share 
#>  0.5486759  0.6323115  0.6742079