igraph: hub_score – R documentation

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hub_score

Kleinberg's hub centrality scores.

Description

The hub scores of the vertices are defined as the principal eigenvector of A*t(A), where A is the adjacency matrix of the graph.

Usage

hub_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 hub scores are the same as authority scores, see authority_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.

Examples

## An in-star
g <- make_star(10)
hub_score(g)$vector

## A ring
g2 <- make_ring(10)
hub_score(g2)$vector

igraph

Network Analysis and Visualization

v1.2.10

GPL (>= 2)

Authors

See AUTHORS file.

Initial release