# R igraph manual pages

Use this if you are using igraph from R

 authority_score {igraph} R Documentation

## Kleinberg's authority centrality scores.

### Description

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:

 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.

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 1.3.2 Index]