Random Graphs: Perform an analysis with random graphs for brain MRI data

Description

analysis_random_graphs performs the steps needed for doing typical graph theory analyses with brain MRI data if you need to generate equivalent random graphs. This includes calculating small world parameters and normalized rich club coefficients.

sim.rand.graph.par simulates N simple random graphs with the same clustering (optional) and degree sequence as the input. Essentially a wrapper for sample_degseq (or, if you want to match by clustering, sim.rand.graph.clust) and make_brainGraph. It uses foreach for parallel processing.

sim.rand.graph.clust simulates a random graph with a given degree sequence and clustering coefficient. Increasing the max.iters value will result in a closer match of clustering with the observed graph.

sim.rand.graph.hqs generates a number of random covariance matrices using the Hirschberger-Qi-Steuer (HQS) algorithm, and create graphs from those matrices.

Usage

analysis_random_graphs(g.list, level = g.list[[1L]]$level, N = 100L,
  savedir = ".", ...)
sim.rand.graph.par(g, level = c("subject", "group"), N = 100L,
  clustering = FALSE, rewire.iters = max(10 * ecount(g), 10000L),
  cl = g$transitivity, max.iters = 100L, ...)
sim.rand.graph.clust(g, rewire.iters = 10000, cl = g$transitivity,
  max.iters = 100)
sim.rand.graph.hqs(resids, level = c("subject", "group"), N = 100L,
  weighted = TRUE, r.thresh = NULL, ...)

Value

analysis_random_graphs returns a list containing:

rich: A data table containing normalized rich-club coefficients and p-values
small: A data table with small-world parameters
rand: A data table with some global graph measures for all random graphs generated

sim.rand.graph.par - a list of N random graphs with some additional vertex and graph attributes

sim.rand.graph.clust - A single igraph graph object

sim.rand.graph.hqs - A list of random graphs from the null covariance matrices

Arguments

g.list: List of brainGraphList objects; the length of this list should equal the number of thresholds/densities in the study
level: Character string indicating whether the graphs are subject-, group-, or contrast-specific. Default: 'subject'
N: Integer; the number of random graphs to simulate. Default: 100
savedir: Character string specifying the directory in which to save the generated graphs. Default: current working directory
...: Other arguments passed to make_brainGraph
g: A graph object
clustering: Logical; whether or not to control for clustering. Default: FALSE
rewire.iters: Integer; number of rewiring iterations for the initial graph randomization. Default: 1e4
cl: The clustering measure. Default: transitivity
max.iters: The maximum number of iterations to perform; choosing a lower number may result in clustering that is further away from the observed graph's. Default: 100
resids: A brainGraph_resids object, a data.table of residuals, or a numeric matrix
weighted: Logical indicating whether to create weighted graphs. If true, a threshold must be provided.
r.thresh: Numeric value for the correlation threshold, if weighted=FALSE.

Author

Christopher G. Watson, cgwatson@bu.edu

Details

analysis_random_graphs does the following:

Generate N random graphs for each graph and density/threshold
Write graphs to disk in savedir. Read them back into R and combine into lists; then write these lists to disk. You can later delete the individual .rds files afterwards.
Calculate small world parameters, along with values for a few global graph measures that may be of interest.
Calculate normalized rich club coefficients and associated p-values.

If you do not want to match by clustering, then simple rewiring of the input graph is performed (the number of rewires equaling the larger of 1e4 and \(10 \times m\), where \(m\) is the graph's edge count).

sim.rand.graph.hqs - The first step is to create the observed covariance of residuals (or whatever matrix/data.table is provided). Then random covariance matrices are created with the same distributional properties as the observed matrix, they are converted to correlation matrices, and finally graphs from these matrices. By default, weighted graphs will be created in which the edge weights represent correlation values. If you want binary matrices, you must provide a correlation threshold.

References

Bansal, S. and Khandelwal, S. and Meyers, L.A. (2009) Exploring biological network structure with clustered random networks. BMC Bioinformatics, 10, 405--421. tools:::Rd_expr_doi("10.1186/1471-2105-10-405")

Hirschberger M., Qi Y., Steuer R.E. (2007) Randomly generating portfolio-selection covariance matrices with specified distributional characteristics. European Journal of Operational Research. 177, 1610--1625. tools:::Rd_expr_doi("10.1016/j.ejor.2005.10.014")

Examples

Run this code

if (FALSE) {
rand_all <- analysis_random_graphs(g.norm, 1e2,
  savedir='/home/cwatson/dti/rand', clustering=F)
}
if (FALSE) {
rand1 <- sim.rand.graph.par(g[[1]][[N]], N=1e3)
rand1.cl <- sim.rand.graph.par(g[[1]][[N]], N=1e2,
  clustering=T, max.iters=1e3)
}

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