nd_extremal: Extremal distance with top-k eigenvalues
In NetworkDistance: Distance Measures for Networks

Description Usage Arguments Value References Examples

Extremal distance (nd.extremal) is a type of spectral distance measures on two graphs' graph Laplacian,

L := D-A

where A is an adjacency matrix and D_{ii}=∑_j A_{ij}. It takes top-k eigenvalues from graph Laplacian matrices and take normalized sum of squared differences as metric. Note that it is 1. non-negative, 2. separated, 3. symmetric, and satisfies 4. triangle inequality in that it is indeed a metric.

1	nd.extremal(A, out.dist = TRUE, k = ceiling(nrow(A)/5))

`A`	a list of length `N` containing adjacency matrices.
`out.dist`	a logical; `TRUE` for computed distance matrix as a `dist` object.
`k`	the number of largest eigenvalues to be used.

a named list containing

D: an (N\times N) matrix or dist object containing pairwise distance measures.
spectra: an (N\times k) matrix where each row is top-k Laplacian eigenvalues.

\insertRef

jakobson_extremal_2002NetworkDistance

## load data
data(graph20)

## compute distance matrix
output = nd.extremal(graph20, out.dist=FALSE, k=2)

## visualize
opar = par(no.readonly=TRUE)
par(pty="s")
image(output$D[,20:1], main="two group case", col=gray(0:32/32), axes=FALSE)
par(opar)