laplace_centr_mult: Calculate Laplacian centrality for a list of graphs.

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

Description

This calculates the Laplacian centrality metric for a graph.

Usage

laplace_centr_mult(
  graphs,
  col.names = NULL,
  row.names = NULL,
  parallel = FALSE,
  cores = NA
)

Arguments

graphs	a list of igraph objects.
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 FALSE. 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

To first understand Laplacian centrality the concept of the Laplacian matrix must be understood. The Laplacian matrix (or graph Laplacian) is the adjacency (or correlation or other weighted connectivity) matrix subtracted from the degree (or strength) matrix. In the strength matrix all entries are zero except for the diagonal, which has as an entry the number corresponding to the degree or strength of node_i.

Mathematically this is represented as

L(G) = X(G) - W(G)

or

L(G) = D(G) - A(G)

The energy of L(G) is used in physics to measure things such as the diffusion of energy through a system and is shown in the formula below:

E_L(G)=∑_{i=1}^nx_i^2+2∑_{i<j}w_{i\text{,}j}^2

Laplacian centrality extends the idea by studying what happens to the ability of energy (or information) to difuse through a network if a node is removed. The centrality score for each node is calculated by the expected drop in energy for the graph Laplacian when node_i is removed. A method of calculating this is given by the formula below:

Δ E_{n}=s_{G}^{2}(n)+s_{G}(n)+2∑_{n _{i}\in N(n)}s_{G}(n_{i})

This measure is very appropriate to the study of brain networks as it can charaterize the expected change in network energy if a region where removed from the brain.

Author(s)

Brandon Vaughan

References

Pauls, S.D., & Remondini, D. (2012). A measure of centrality based on the spectrum of the Laplacian. Physical review. E, Statistical, nonlinear, and soft matter physics, 85 6 Pt 2, 066127.

Qi, Xingqin, et al. (2012). Laplacian centrality: A new centrality measure for weighted networks. Information Sciences 194: 240-253.

See Also

laplace_centr leverage_centr leverage_centr_mult

Examples

laplace_centr_mult(graphs, parallel=FALSE) # If you only have two cores parallel=FALSE is a good idea.

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