graph.entropy: Graph spectral entropy

In statGraph: Statistical Methods for Graphs

Description

graph.entropy returns the spectral entropy of an undirected graph.

Usage

graph.entropy(G = NULL, bandwidth = "Silverman", eigenvalues = NULL)

Arguments

G	the undirected graph (igraph type) or its adjacency matrix. 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.
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.
eigenvalues	optional parameter. It contains the eigenvalues of matrix G. Then, if the eigenvalues of matrix G have already been computed, this parameter can be used instead of G. If no value is passed, then the eigenvalues of G will be computed by 'graph.entropy'.

Value

a real number corresponding to the graph spectral entropy.

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

G <- igraph::sample_gnp(n=100, p=0.5)
entropy <- graph.entropy(G)
entropy

statGraph documentation built on May 19, 2021, 9:11 a.m.