hub_score
Kleinberg's hub centrality scores.
The hub scores of the vertices are defined as the principal eigenvector of \(A A^T\), where \(A\) is the adjacency matrix of the graph.
Usage
hub_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. This function interprets edge weights as connection strengths. In the random surfer model, an edge with a larger weight is more likely to be selected by the surfer.- options
A named list, to override some ARPACK options. See
arpackfor details.
Details
For undirected matrices the adjacency matrix is symmetric and the hub
scores are the same as authority scores, see
authority_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
authority_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)$vector
## A ring
g2 <- make_ring(10)
hub_score(g2)$vector
# }