authority_score {igraph} | R Documentation

## Kleinberg's authority centrality scores.

### Description

The authority scores of the vertices are defined as the principal eigenvector of t(A)*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:

`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.

### 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

    ## 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

[Package igraph version 1.1.2 Index]