[igraph] Negative eigenvalues of a laplacian matrix

[MATSUDA, Noriyuki]

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.