Re: [igraph] Negative eigenvalues of a laplacian matrix

[MATSUDA, Noriyuki]

Gabor:

  Thanks a lot.

On 2008/07/14, at 18:47, Gabor Csardi wrote:

> Ok, the results are all right for me, this is about numeric accuracy
> only. These are the smallest eigenvalues:
>
> [106]  6.992917e-01  4.151255e-01  5.454894e-15  6.661338e-16   
> 6.661338e-16
> [111]  3.522995e-16  4.097342e-17  3.422020e-17  0.000000e+00  
> -9.300142e-17
>
> The last eight are zero, that means that there are eight components
> in the graph:
>
> > no.clusters(cg)
> [1] 8
>
> Probably you want to round the 'almost zero' values to zero:
>
> eig$values <- ifelse(eig$values > 1e-14, eig$values, 0)
>
> G.
>
> On Mon, Jul 14, 2008 at 06:35:27PM +0900, MATSUDA, Noriyuki wrote:
> > 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 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
> [...]
>
> --
> Csardi Gabor <address@hidden>    UNIL DGM
>
>
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MATSUDA, Noriyuki  <Kanji> 松田紀之