# scg_eps

##### Error of the spectral coarse graining (SCG) approximation

`scg_eps`

computes \(\Vert v_i-Pv_i\Vert\), where
\(v_i\) is the \(i\)th eigenvector in `V`

and \(P\) is the
projector corresponding to the `mtype`

argument.

##### Usage

```
scg_eps(V, groups, mtype = c("symmetric", "laplacian", "stochastic"),
p = NULL, norm = c("row", "col"))
```

##### Arguments

- V
A numeric matrix of (eigen)vectors assumed normalized. The vectors are to be stored column-wise in

`V`

).- groups
A vector of

`nrow(V)`

integers labeling each group vertex in the partition.- mtype
The type of semi-projector used for the SCG. For now “symmetric”, “laplacian” and “stochastic” are available.

- p
A probability vector of length

`nrow(V)`

.`p`

is the stationary probability distribution of a Markov chain when`mtype`

= “stochastic”. This parameter is ignored otherwise.- norm
Either “row” or “col”. If set to “row” the rows of the Laplacian matrix sum to zero and the rows of the stochastic matrix sum to one; otherwise it is the columns.

##### Value

`scg_eps`

returns with a numeric vector whose \(i\)th
component is \(\Vert v_i-Pv_i\Vert\) (see Details).

##### References

D. Morton de Lachapelle, D. Gfeller, and P. De Los Rios,
Shrinking Matrices while Preserving their Eigenpairs with Application to the
Spectral Coarse Graining of Graphs. Submitted to *SIAM Journal on
Matrix Analysis and Applications*, 2008.
http://people.epfl.ch/david.morton

##### See Also

scg-method and `scg`

.

##### Examples

```
# NOT RUN {
v <- rexp(20)
km <- kmeans(v,5)
sum(km$withinss)
scg_eps(cbind(v), km$cluster)^2
# }
```

*Documentation reproduced from package igraph, version 1.0.1, License: GPL (>= 2)*