# 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

`weight`

edge 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

`arpack`

for 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
# }
```

*Documentation reproduced from package igraph, version 1.2.4.2, License: GPL (>= 2)*