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Re: [igraph] Negative eigenvalues of a laplacian matrix
From: |
Gabor Csardi |
Subject: |
Re: [igraph] Negative eigenvalues of a laplacian matrix |
Date: |
Mon, 14 Jul 2008 04:04:34 -0500 |
User-agent: |
Mutt/1.5.17+20080114 (2008-01-14) |
On Mon, Jul 14, 2008 at 06:00:10PM +0900, MATSUDA, Noriyuki wrote:
> Hello:
>
> I am having a problem with my graph which produces negative
> eigenvalues of its laplacian matrix:
> graph in Rdata : http:www.sk.tsukuba.ac.jp/~mazda/dA/cg.Rdata
It is not really here:
address@hidden:/tmp$ wget http://www.sk.tsukuba.ac.jp/~mazda/dA/cg.Rdata
--04:02:45-- http://www.sk.tsukuba.ac.jp/~mazda/dA/cg.Rdata
=> `cg.Rdata'
Resolving www.sk.tsukuba.ac.jp... 130.158.96.30
Connecting to www.sk.tsukuba.ac.jp|130.158.96.30|:80... connected.
HTTP request sent, awaiting response... 302 Found
Location: http://infoshako.sk.tsukuba.ac.jp/~mazda/dA/cg.Rdata [following]
--04:02:45-- http://infoshako.sk.tsukuba.ac.jp/~mazda/dA/cg.Rdata
=> `cg.Rdata'
Resolving infoshako.sk.tsukuba.ac.jp... 130.158.97.229
Connecting to infoshako.sk.tsukuba.ac.jp|130.158.97.229|:80... connected.
HTTP request sent, awaiting response... 404 Not Found
04:02:46 ERROR 404: Not Found.
> graph plot: http:www.sk.tsukuba.ac.jp/~mazda/dA/cg.Rdata
> Rscript:
> library(igraph)
> load(file="..../cg.Rdata)
> lap <- graph.laplacian(cg)
> eig <- eigen(lap)
> Results: the smallest three eigen values
> 0.000, -1.822e-15, -7.549e-15
These are not negative, these are in reality zero, only the numeric
precision/computation makes them look like negative.
> The problem:
> All the eigenvalues of a laplacian matrix are non-negative
> according to the references, e.g.,
> http://www.cs.berkeley.edu/~demmel/cs267/lecture20/
> lecture20.html
> The possible cause:
> eig[,113] is zero with an exception of eig[114,113]=-1
>
> I'd greatly appreciate any help.
Please check your data file and I'll check it.
Gabor
>
>
>
>
> _______________________________________________
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--
Csardi Gabor <address@hidden> UNIL DGM