Thanks for your reply.
It seems like that I can intensify the tension. :) I was thinking that there is no way that the subgraph of cluster 293815 is the only star schemed subgraph so I tried to find an other one. And I found more than one. I examined the cluster nr 293812 and it looks like the same as the nr 293815 but here I can calculate the authority score.
> g_sub[293815]
$`293815`
IGRAPH U-W- 4 3 --
+ attr: weight (e/n)
+ edges:
[1] 1--2 1--3 1--4
> g_sub[293812]
$`293812`
IGRAPH U-W- 4 3 --
+ attr: weight (e/n)
+ edges:
[1] 1--4 2--4 3--4
> E(g_sub[[293815]])$weight
[1] 270 5677 3032
> E(g_sub[[293812]])$weight
[1] 3696 1206 642
> m15 = as.matrix(get.adjacency(g_sub[[293815]], attr="weight"))
> m12 = as.matrix(get.adjacency(g_sub[[293812]], attr="weight"))
> m15
[,1] [,2] [,3] [,4]
[1,] 0 270 5677 3032
[2,] 270 0 0 0
[3,] 5677 0 0 0
[4,] 3032 0 0 0
> m12
[,1] [,2] [,3] [,4]
[1,] 0 0 0 3696
[2,] 0 0 0 1206
[3,] 0 0 0 642
[4,] 3696 1206 642 0
> eigen(m15 %*% t(m15))$vector
[,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
> eigen(m12 %*% t(m12))$vector
[,1] [,2] [,3] [,4]
[1,] 0 0.9379679 0.3467222 0.0000000
[2,] 0 0.3060577 -0.8279605 -0.4699043
[3,] 0 0.1629262 -0.4407551 0.8827174
[4,] 1 0.0000000 0.0000000 0.0000000
> eigen(m15 %*% t(m15))$value
[1] 4.149425e+07 4.149425e+07 7.450581e-09 1.862645e-09
> eigen(m12 %*% t(m12))$value
[1] 1.552702e+07 1.552702e+07 1.303852e-08 0.000000e+00
> authority_score(g_sub[[293815]])$vector
Error in .Call("R_igraph_authority_score", graph, scale, weights, options, :
At arpack.c:944 : ARPACK error, No shifts could be applied during a cycle of the Implicitly restarted Arnoldi iteration. One possibility is to increase the size of NCV relative to NEV
> authority_score(g_sub[[293812]])$vector
[1] 0.43989186 0.14353614 0.07640979 1.00000000
So the two graph have the same structure and both of them have dominant eigenvalues with multiplicity 2, but the authority score fails on the first one (g_sub[293815]) but succeed on the second one (g_sub[2938152). I don't get it. Am I missing something?
Another thing: can be installing arpack-ng a solution for the arpack fails?
https://github.com/pv/arpack-ng
Best regards,
Adam Sohonyai