centr_lev: Calculate a vertex's leverage centrality

In cwatson/brainGraph: Graph Theory Analysis of Brain MRI Data

Calculate a vertex's leverage centrality

Description

Calculates the leverage centrality of each vertex in a graph.

Usage

centr_lev(g, A = NULL)

Arguments

g	An igraph graph object
A	Numeric matrix; the adjacency matrix of the input graph. Default: NULL

Details

The leverage centrality relates a vertex's degree with the degree of its neighbors. The equation is:

l_i = \frac{1}{k_i} \sum_{j \in N_i} \frac{k_i - k_j}{k_i + k_j}

where k_i is the degree of the i^{th} vertex and N_i is the set of neighbors of i. This function replaces NaN with NA (for functions that have the argument na.rm).

Value

A vector of the leverage centrality for all vertices.

Author(s)

Christopher G. Watson, [e-mail]

References

Joyce, K.E. and Laurienti P.J. and Burdette J.H. and Hayasaka S. (2010) A new measure of centrality for brain networks. PLoS One, 5(8), e12200. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1371/journal.pone.0012200")}

See Also

Other Centrality functions: centr_betw_comm

cwatson/brainGraph documentation built on Feb. 21, 2024, 6:33 p.m.