kleinberg: Kleinberg's centrality scores.

Description

Kleinberg's hub and authority scores.

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.

Value

A named list with members:
vectorThe authority/hub scores of the vertices.
valueThe corresponding eigenvalue of the calculated principal eigenvector.
optionsSome 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

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.

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

Run this code

## 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

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