Finds blocks of nodes with intra-positive and inter-negative edges

## Arguments

- g
igraph object with a sign edge attribute.

- k
number of blocks

- alpha
see details

- annealing
logical. if TRUE, use simulated annealing (Default: FALSE)

## Details

The function minimizes P(C)=\(\alpha\)N+(1-\(\alpha\))P, where N is the total number of negative ties within plus-sets and P be the total number of positive ties between plus-sets. This function implements the structural balance model. That is, all diagonal blocks are positive and off-diagonal blocks negative. For the generalized version see signed_blockmodel_general.

## References

Doreian, Patrick and Andrej Mrvar (2009). Partitioning signed social networks. *Social Networks* 31(1) 1-11

## Examples

```
library(igraph)
g <- sample_islands_signed(10, 10, 1, 20)
clu <- signed_blockmodel(g, k = 10, alpha = 0.5)
table(clu$membership)
#>
#> 1 2 3 4 5 6 7 8 10
#> 11 11 11 12 11 10 10 13 11
clu$criterion
#> [1] 49
# Using simulated annealing (less change of getting trapped in local optima)
data("tribes")
clu <- signed_blockmodel(tribes, k = 3, alpha = 0.5, annealing = TRUE)
table(clu$membership)
#>
#> 1 2 3
#> 7 5 4
clu$criterion
#> [1] 2
```