statGraph (version 0.5.1)

takahashi.test: Test for the Jensen-Shannon divergence between graphs

Description

takahashi.test tests whether two sets of graphs were generated by the same random graph model. This bootstrap test is based on the Jensen-Shannon (JS) divergence between graphs.

Usage

takahashi.test(G1, G2, maxBoot = 1000, bandwidth = "Silverman")

Value

A list containing:

JSD

the Jensen-Shannon divergence between 'G1' and 'G2'.

p.value

the p-value of the test.

Arguments

G1

a list of undirected graphs (igraph type) or their adjacency matrices. The adjacency matrix of an unweighted graph contains only 0s and 1s, while the weighted graph may have nonnegative real values that correspond to the weights of the edges.

G2

a list of undirected graphs (igraph type) or their adjacency matrices. The adjacency matrix of an unweighted graph contains only 0s and 1s, while the weighted graph may have nonnegative real values that correspond to the weights of the edges.

maxBoot

integer indicating the number of bootstrap resamplings.

bandwidth

string showing which criterion is used to choose the bandwidth during the spectral density estimation. Choose between the following criteria: "Silverman" (default), "Sturges", "bcv", "ucv" and "SJ". "bcv" is an abbreviation of biased cross-validation, while "ucv" means unbiased cross-validation. "SJ" implements the methods of Sheather & Jones (1991) to select the bandwidth using pilot estimation of derivatives.

Details

Given two lists of graphs, 'G1' and 'G2', 'takahashi.test' tests H0: "JS divergence between 'G1' and 'G2' is 0" against H1: "JS divergence between 'G1' and 'G2' is larger than 0".

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)
G1 <- G2 <- list()
for (i in 1:20) {
  G1[[i]] <- igraph::sample_gnp(n=50, p=0.5)
}
for (i in 1:20) {
  G2[[i]] <- igraph::sample_gnp(n=50, p=0.51)
}
result <- takahashi.test(G1, G2, maxBoot=100)
result