leverage_centr: Calculate leverage centrality for a single graph..

In abnormally-distributed/rsfcNet: Analyze resting state functional connectivity networks

Description

This function calculates the leverage centrality for a single graph.

Usage

leverage_centr(graph, weighted = TRUE, strength.star = F)

Arguments

graph	An undirected igraph object.
weighted	By default TRUE, but can also be set to FALSE.
strength.star	Should the strength* measure of Rubinov & Sporns (2011) be used? Defaults to FALSE. If set to TRUE, only positive weights are used. Only applicable when weighted = TRUE.

Details

Leverage centrality is a new measure of node centrality put forth by Joyce et al (2010). Developed specifically for use in functional brain network analysis, this measure has a favorable property of attempting to chracterize information flow in an undirected functional brain network. Leverage centrality compares the degree of a node to the degree of all its neighbors. A node with a high degree/strength is not necessarily one with a high centrality value. Leverage centrality defines centrality as having high degree/strength relative to the degree/strength of a node's neighbors. If the neighbors are also of high degree/strength the node is not considered a central node. Keeping with its biological inspiration, leverage centrality does not assume information in a network flows in a serial fashion or only along the shortest path, but on how information flows within a local neighborhood of nodes (Joyce et al, 2010).

The formula for leverage centrality is given below, where k_i is the degree/strength of a node and k_j is the degree/strength of its neighbors.

L = \frac{1}{k_i} ∑_N_i \frac{k_i-k_j}{k_i+k_j}

For more information on the mathematics of leverage centrality see Vargas et al (2017). This function was originally written by Alex Upton and can be found on the igraph wiki (see references).

Value

A matrix of the leverage centralities of each node in a subject.

Author(s)

Alex Upton, Brandon Vaughan

References

Joyce, K. E., Laurienti, P. J., Burdette, J. H., & Hayasaka, S. (2010). A New Measure of Centrality for Brain Networks. PLoS ONE, 5(8). doi:10.1371/journal.pone.0012200

Rubinov, M., & Sporns, O. (2011). Weight-conserving characterization of complex functional brain networks. NeuroImage, 56(4), 2068-2079. doi:10.1016/j.neuroimage.2011.03.069

Vargas, R., Waldron, A., Sharma, A., Flórez, R., & Narayan, D. A. (2017). A graph theoretic analysis of leverage centrality. AKCE International Journal of Graphs and Combinatorics, 14(3), 295-306. doi:10.1016/j.akcej.2017.05.001

http://igraph.wikidot.com/r-recipes#toc10

Examples

leverage_centr(binary.graph, weighted=FALSE)
leverage_centr(weighted.graph, weighted=TRUE)

abnormally-distributed/rsfcNet documentation built on March 8, 2020, 5:32 p.m.