Laplacian Experiments/Eigenvectors

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(07:33, 20 June 2013)

Setting out to visualize eigenvectors of a graph's Laplacian matrix. A work in progress...

double.star.eigenvectors.Rstep

prereq: $(MF)/double.star.graph.R $(MF)/laplacian.functions.R $(MF)/graph.plotting.functions.R
library(network)
G <- double.star.graph()
Le <- standard.laplacian(as.matrix(G))
Le.eig <- eigen(Le)
print(Le.eig)
coord <- NULL
for (i in 1:ncol(Le.eig[['vectors']]))
{ coord <- plot.vertex.function(G,sapply(Le.eig[['vectors']][,i],make.edge.color),
    paste('double.star.eigen.',i,'.png',sep=''),coord=coord)
}

WorkingWiki messages

Here are the 10 eigenvectors of the standard Laplacian matrix of the double-star network, in no particular order.

I'm using black/gray for positive numbers, and red/pink for negative, blending into white near zero.

It looks like the last one is the dominant eigenvalue (all entries equal), and the second-to-last one is the "Fiedler vector" that you would use for clustering.