kleinberg: Kleinberg's centrality scores.
Description
Kleinberg's hub and authority scores.Usage
authority.score (graph, scale = TRUE, weights=NULL, options = igraph.arpack.default)
hub.score (graph, scale = TRUE, weights=NULL, options = igraph.arpack.default)
Arguments
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 weight
edge
attribute, then this is used by default.
options
A named list, to override some ARPACK options. See
arpack
for details. Value
- A named list with members:
- vectorThe authority/hub scores of the vertices.
- valueThe corresponding eigenvalue of the calculated
principal eigenvector.
- optionsSome information about the ARPACK computation, it has
the same members as the
options
member returned by
arpack
, see that for documentation.
concept
Hub and authority scoreDetails
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. 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.
Obviously, for undirected matrices the adjacency matrix is symmetric
and the two scores are the same.
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
evcent
for eigenvector centrality,
page.rank
for the Page Rank scores. arpack
for the underlining machinery of the computation.Examples
Run this code## An in-star
g <- graph.star(10)
hub.score(g)$vector
authority.score(g)$vector
## A ring
g2 <- graph.ring(10)
hub.score(g2)$vector
authority.score(g2)$vector
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