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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...
Connecting to www.sk.tsukuba.ac.jp||: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...
Connecting to infoshako.sk.tsukuba.ac.jp||: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.


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Csardi Gabor <address@hidden>    UNIL DGM

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