nd.wsd {NetworkDistance}

Distance with Weighted Spectral Distribution

Description

Normalized Laplacian matrix contains topological information of a corresponding network via its spectrum. nd.wsd adopts weighted spectral distribution of eigenvalues and brings about a metric via binning strategy.

Usage

nd.wsd(A, out.dist = TRUE, K = 50, wN = 4)

Arguments

A

a list of length N containing (M\times M) adjacency matrices.

out.dist

a logical; TRUE for computed distance matrix as a dist object.

K

the number of bins for the spectrum interval [0,2].

wN

a decaying exponent; default is 4 set by authors.

Value

a named list containing

D

an (N\times N) matrix or dist object containing pairwise distance measures.

spectra

an (N\times M) matrix of rows being eigenvalues for each graph.

References

Fay D, Haddadi H, Thomason A, Moore AW, Mortier R, Jamakovic A, Uhlig S, Rio M (2010). “Weighted Spectral Distribution for Internet Topology Analysis: Theory and Applications.” IEEE/ACM Transactions on Networking, 18(1), 164–176. ISSN 1063-6692, 1558-2566.

Examples

## load example data and extract a few
data(graph20)
gr.small = graph20[c(1:5,11:15)]

## compute distance matrix
output = nd.wsd(gr.small, out.dist=FALSE, K=10)

## visualize
opar = par(no.readonly=TRUE)
par(pty="s")
image(output$D[,10:1], main="two group case", axes=FALSE, col=gray(0:32/32))
par(opar)