Re: [igraph] Performance issue regarding when calculating induced_subgra

[Tamas Nepusz]

Hi,

Further analysis of your graph shows that ARPACK fails to converge
because the dominant eigenvalue has multiplicity > 1:

> m <- get.adjacency(g, attr="weight")
> m
4 x 4 sparse Matrix of class "dgCMatrix"

[1,]    . 270 5677 3032
[2,]  270   .    .    .
[3,] 5677   .    .    .
[4,] 3032   .    .    .
> eigen(m %*% t(m))
$values
[1] 4.149425e+07 4.149425e+07 7.450581e-09 1.862645e-09

$vectors
     [,1]        [,2]        [,3]       [,4]
[1,]    1  0.00000000  0.00000000  0.0000000
[2,]    0 -0.04191503  0.99912118  0.0000000
[3,]    0 -0.88130233 -0.03697231 -0.4711043
[4,]    0 -0.47069027 -0.01974635  0.8820775

Since the dominant eigenvalue has multiplicity 2, it means that any
vector that is a linear combination of the first and second
eigenvector is also a valid eigenvector, thus there is no unique
solution of the equation for the authority score.

T.


On Tue, May 3, 2016 at 12:59 PM, Tamas Nepusz <address@hidden> wrote:
>> This is fine, but note that the hub and authority scores are equal to
>> each other _and_ to the eigenvector centrality in undirected graphs,
> Scratch that - the hub and authority scores are indeed equal to each
> other, but the eigenvector centrality seems to be different, although
> I don't quite understand why. Hmmm. Let me think about this.
>
> T.