graph.mult.scaling {statGraph}

Multidimensional Scaling of Graphs

Description

graph.mult.scaling performs multidimensional scaling of graphs. It takes the Jensen-Shannon divergence between graphs (JS) and uses the cmdscale function from the stats package to obtain a set of points such that the distances between the points are similar to JS.

Usage

graph.mult.scaling(
  Graphs,
  plot = TRUE,
  type = "n",
  dist = "JS",
  main = "",
  ...
)

Arguments

Graphs

a list of undirected graphs. If each graph has the attribute eigenvalues containing its eigenvalues , such values will be used to compute their spectral density.

plot

logical. If TRUE (default) the points chosen to represent the Jensen-Shannon divergence between graphs are plotted.

type

what type of plot should be drawn. The default value is 'n', which indicates that the points will not be plotted (i. e. only the labels of the graphs will be plotted).

dist

string indicating if you want to use the 'JS' (default), 'L1' or 'L2' distances. 'JS' means Jensen-Shannon divergence.

main

title of the plot (default value is ”).

...

additional parameters for graph.spectral.density.

Value

A list with class 'statGraph' containing the following components:

method:

a string indicating the used method.

info:

a string showing details about the method.

data.name:

a string with the data's name(s).

values:

a matrix in which each column corresponds to a coordinate and each row corresponds to a graph (point). Then, each row gives the coordinates of the points chosen to represent the Jensen-Shannon divergence (by default), L1, or L2 distance between graphs.

References

Takahashi, D. Y., Sato, J. R., Ferreira, C. E. and Fujita A. (2012) Discriminating Different Classes of Biological Networks by Analyzing the Graph Spectra Distribution. _PLoS ONE_, *7*, e49949. doi:10.1371/journal.pone.0049949.

Silverman, B. W. (1986) _Density Estimation_. London: Chapman and Hall.

Sturges, H. A. The Choice of a Class Interval. _J. Am. Statist. Assoc._, *21*, 65-66.

Sheather, S. J. and Jones, M. C. (1991). A reliable data-based bandwidth selection method for kernel density estimation. _Journal of the Royal Statistical Society series B_, 53, 683-690. http://www.jstor.org/stable/2345597.

Examples

set.seed(1)
G <- list()
for (i in 1:5) {
  G[[i]] <- igraph::sample_gnp(50, 0.5)
}
for (i in 6:10) {
  G[[i]] <- igraph::sample_smallworld(1, 50, 8, 0.2)
}
for (i in 11:15) {
  G[[i]] <- igraph::sample_pa(50, power = 1, directed = FALSE)
}
graph.mult.scaling(G)