authority_score
Kleinberg's authority centrality scores.
The authority scores of the vertices are defined as the principal eigenvector of \(A^T A\), where \(A\) is the adjacency matrix of the graph.
Usage
authority_score(graph, scale = TRUE, weights = NULL,
options = arpack_defaults)Arguments
- graph
The input graph.
- scale
Logical scalar, whether to scale the result to have a maximum score of one. If no scaling is used then the result vector has unit length in the Euclidean norm.
- weights
Optional positive weight vector for calculating weighted scores. If the graph has a
weightedge attribute, then this is used by default.- options
A named list, to override some ARPACK options. See
arpackfor details.
Details
For undirected matrices the adjacency matrix is symmetric and the
authority scores are the same as hub scores, see
hub_score.
Value
A named list with members:
The authority/hub scores of the vertices.
The corresponding eigenvalue of the calculated principal eigenvector.
Some information about the ARPACK computation, it has
the same members as the options member returned
by arpack, see that for documentation.
References
J. Kleinberg. Authoritative sources in a hyperlinked environment. Proc. 9th ACM-SIAM Symposium on Discrete Algorithms, 1998. Extended version in Journal of the ACM 46(1999). Also appears as IBM Research Report RJ 10076, May 1997.
See Also
hub_score, eigen_centrality for
eigenvector centrality, page_rank for the Page Rank
scores. arpack for the underlining machinery of the
computation.
Examples
# NOT RUN {
## An in-star
g <- make_star(10)
hub_score(g)$vector
authority_score(g)$vector
## A ring
g2 <- make_ring(10)
hub_score(g2)$vector
authority_score(g2)$vector
# }