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## [igraph] Negative eigenvalues of a laplacian matrix

**From**: |
MATSUDA, Noriyuki |

**Subject**: |
[igraph] Negative eigenvalues of a laplacian matrix |

**Date**: |
Mon, 14 Jul 2008 18:00:10 +0900 |

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
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
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.

`
``
``
`