leverage_centr_mult: Calculate leverage centrality for a list of graphs.

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

Description

This function calculates the leverage centrality for multiple graphs.

Usage

leverage_centr_mult(
  graphs,
  weighted = TRUE,
  strength.star = F,
  col.names = NULL,
  row.names = NULL,
  parallel = TRUE,
  cores = NA
)

Arguments

graphs	a list of igraph objects.
weighted	By default weighted=FALSE, but can also be set to weighted=TRUE.
col.names	The names of each column (node labels).
row.names	The names of each row (subject).
parallel	Should multiple cores be used? Defaults to TRUE. If TRUE, progress bar is not displayed. This is normal.
cores	How many cores should be used? Defaults to recommended 1 less than number of CPU cores.

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). What this function changes is replacing NaN with zero in the case where a node without any connections after thresholding results in divison by zero. This function also expands leverage centrality to weighted undirected networks. If doing this, be sure to threshold the correlation matrix per Joyce et al (2010).

Value

A matrix of the leverage centralities of each node for each 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

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

See Also

leverage_centr laplace_centr laplace_centr_mult

Examples

leverage_centr_mult(binary.graphs, weighted=FALSE)
leverage_centr_mult(weighted.graphs, weighted=TRUE)

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