NetworkDistance (version 0.3.6)

nd.extremal: Extremal distance with top-\(k\) eigenvalues

Description

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 \(D_{ii}=\sum_j A_{ij}\). 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.

Usage

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

Value

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.

Arguments

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.

References

jakobson_extremal_2002NetworkDistance

Examples

# \donttest{
## 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)
# }