summary_centrality_kleinberg: Kleinberg's hub and authority centrality scores.

In drostlab/edgynode: Comparison of Gene Regulatory Networks

Kleinberg's hub and authority centrality scores.

Description

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.

Usage

summary_centrality_kleinberg(graph, mode = "hub", scale = TRUE, weights = NULL)

Arguments

graph	The input graph.
mode	Wether to calculate the hub or authority score (default:hub)
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.

Details

Similarly, 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.

For undirected matrices the adjacency matrix is symmetric and the hub scores are the same as authority scores.

Value

A named list with members:

vector	The hub or authority 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

[eigen_centrality()] for eigenvector centrality, [page_rank()] for the Page Rank scores. [arpack()] for the underlining machinery of the computation.

drostlab/edgynode documentation built on March 29, 2024, 10:36 a.m.