Re: [igraph] Negative eigenvalues of a laplacian matrix

[MATSUDA, Noriyuki]

Sorry:

   Here are the correct URL:
     http://www.sk.tsukuba.ac.jp/~mazda/dUG/dA/cg.Rdata
     http://www.sk.tsukuba.ac.jp/~mazda/dUG/dA/cg.pdf

On 2008/07/14, at 18:04, Gabor Csardi wrote:

> 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
>
> > _______________________________________________
> > igraph-help mailing list
> > address@hidden
> > http://lists.nongnu.org/mailman/listinfo/igraph-help
>
> --
> Csardi Gabor <address@hidden>    UNIL DGM
>
>
> _______________________________________________
> igraph-help mailing list
> address@hidden
> http://lists.nongnu.org/mailman/listinfo/igraph-help

MATSUDA, Noriyuki  <Kanji> 松田紀之