# kleinberg

##### Kleinberg's centrality scores.

Kleinberg's hub and authority scores.

- Keywords
- graphs

##### Usage

```
authority.score (graph, scale = TRUE, weights=NULL, options = igraph.arpack.default)
hub.score (graph, scale = TRUE, weights=NULL, 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.
- 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.

##### 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. value The corresponding eigenvalue of the calculated principal eigenvector. options Some 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.

##### See Also

`evcent`

for eigenvector centrality,
`page.rank`

for the Page Rank scores. `arpack`

for the underlining machinery of the computation.

##### 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 0.6.5-2, License: GPL (>= 2)*