# kleinberg

0th

Percentile

##### Kleinberg's centrality scores.

Kleinberg's hub and authority scores.

Keywords
graphs
##### Usage
authority.score (graph, scale = TRUE, options = igraph.arpack.default)
hub.score (graph, scale = TRUE, options = igraph.arpack.default)
##### 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.
options
A named list, to override some ARPACK options. See arpack for details.
##### Details

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.

##### Value

• A named list with members:
• vector
{The 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 score

##### 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.

evcent for eigenvector centrality, page.rank for the Page Rank scores. arpack for the underlining machinery of the computation.

##### Aliases
• authority.score
• hub.score
##### Examples
## 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
Documentation reproduced from package igraph, version 0.5.1, License: GPL (>= 2)

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