statGraph (version 0.5.1)

sp.anogva: Semi-Parametric Analysis Of Graph Variability (ANOGVA)

Description

sp.anogva statistically tests whether two or more graphs are generated by the same model and set of parameters.

Usage

sp.anogva(
  G,
  model,
  maxBoot = 500,
  spectra = NULL,
  eps = 0.01,
  classic = FALSE,
  bandwidth = "Silverman"
)

Value

A list containing:

parameters

a vector containing the estimated parameters for each graph.

F.value

the F statistic of the test.

p.value

the p-value of the test.

Arguments

G

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.

model

A string that indicates one of the following models: "ER" (Erdos-Renyi random graph model), "GRG" (geometric random graph model), "WS" (Watts-Strogatz random graph model), and "BA" (Barabasi-Albert random graph model).

maxBoot

integer indicating the number of bootstrap resamples (default is 500).

spectra

optional parameter containing the precomputed spectrum of the model. It is a three-dimensional array in which the first dimension corresponds to all parameters that will be explored in the parameter estimation, the second dimension has the same size of the given graph, and the third one corresponds to graphs randomly generated by the model. Thus, the position (i,j,k) contains the j-th eigenvalue of the k-th graph generated with the i-th parameter. The attribute 'rownames' of the array corresponds to the parameters converted to string. If spectra is NULL (default), then model' is used to generate random graphs and their spectra are computed automatically.

eps

(default is 0.01) precision of the grid when 'classic' = TRUE.

classic

logical. If FALSE (default) parameter is estimated using ternary search, if TRUE parameter is estimated using grid search.

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.

References

Andre Fujita, Eduardo Silva Lira, Suzana de Siqueira Santos, Silvia Yumi Bando, Gabriela Eleuterio Soares, Daniel Yasumasa Takahashi. A semi-parametric statistical test to compare complex networks, Journal of Complex Networks, cnz028, https://doi.org/10.1093/comnet/cnz028

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

if (FALSE) {
set.seed(42)
model <- "ER"
G <- list()

# Under H0
G[[1]] <- igraph::sample_gnp(50, 0.5)
G[[2]] <- igraph::sample_gnp(50, 0.5)
G[[3]] <- igraph::sample_gnp(50, 0.5)
result1 <- sp.anogva(G, model, maxBoot = 300)
result1

# Under H1
G[[1]] <- igraph::sample_gnp(50, 0.5)
G[[2]] <- igraph::sample_gnp(50, 0.55)
G[[3]] <- igraph::sample_gnp(50, 0.5)
result2 <- sp.anogva(G, model, maxBoot = 300)
result2
}