HITS hubs and authorities

Kleinberg's I and O operations applied alternately, each pair of updates followed by a normalisation to unit L2 norm. In matrix form a = A' h and h = A a, so the authority vector converges to the principal eigenvector of A'A and the hub vector to that of A A'.

Usage

Hits(A, iters = 50)

Arguments

A

Square adjacency matrix, A[i, j] > 0 for a link i -> j.

iters

Number of I/O sweeps, at least one.

Value

List with estimate (largest hub score), hubs, authorities, top_hub, n, iters, method.

Details

Formula: a <- A' h; h <- A a; both rescaled to unit L2 norm.

References

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

Examples

Hits(matrix(c(0, 1, 1, 0, 0, 1, 1, 0, 0), 3, 3, byrow = TRUE))
#> $estimate
#> [1] 0.8506508
#> 
#> $hubs
#> [1] 8.506508e-01 5.257311e-01 9.172696e-22
#> 
#> $authorities
#> [1] 1.484173e-21 5.257311e-01 8.506508e-01
#> 
#> $top_hub
#> [1] 1
#> 
#> $n
#> [1] 3
#> 
#> $iters
#> [1] 50
#> 
#> $method
#> [1] "alternating I/O operations of Kleinberg (1999) sect. 3, L2-normalised"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"