nd_wsd function

Distance with Weighted Spectral Distribution

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.

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.

Returns

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.

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)

References

Rdpack::insert_ref(key="fay_weighted_2010",package="NetworkDistance")