# sedist: Computes distances in terms of Structural equivalence... In blockmodeling: An R package for generalized and classical blockmodeling of valued networks

## Description

The functions computed the distances in terms of Structural equivalence (Lorrain and White, 1971) between the units of a one-mode network. Several options for treating the diagonal values are supported.

## Usage

 ```1 2 3``` ```sedist(M, method = "default", fun = "default", fun.on.rows = "default", handle.interaction = "switch", use = "pairwise.complete.obs", ...) ```

## Arguments

 `M` A matrix representing the (usually valued) network. For now, only one-relational networks are supported. The network must be one-mode. `method` The method used to compute distances - any of the methods allowed by functions dist, cor or cov all package::stats or just "cor" or "cov" (given as character). `fun` Which function should be used to compute distances (given as character), . `fun.on.rows` For non-standard function - does the function compute measure on rows (such as `cor`, `cov`,...) of the data matrix (as opposed to computing measure on columns (such as `dist`). `handle.interaction` How should the interaction between the vertices analysed be handled: "switch" (the default) - assumes that when comparing units i and j, M[i,i] should be compared with M[j,j] and M[i,j] with M[j,i]. This two comparisons are weighted by 2. This should be used with euclidean distance to get the corrected euclidean distance with p = 2. "switch2" - the same (alias) "switch1" - the same as above, only that the two comparisons are weighted by 1. This should be used with euclidean distance to get the corrected euclidean distance with p = 1. "ignore" (diagonal) - Diagonal is ignored. This should be used with euclidean distance to get the corrected euclidean distance with p = 0. "none" - the matrix is used "as is" `use` For use with methods "cor" and "cov", for other methods (the default option should be used if handle.interaction=="ignore"), "pairwise.complete.obs" are always used, if stats.dist.cor.cov=TRUE `...` Additional arguments to `fun`

## Details

If both `method` and `fun` are "default", the euclidean distances are computed. the "default" method for `fun="dist"` is "euclidean" and for `fun="cor"` "pearson".

## Value

A matrix (usually of class dist) is returned.

## Author(s)

Ale<c5><a1> <c5><bd>iberna

## References

Batagelj, V., Ferligoj, A., Doreian, P. (1992): Direct and indirect methods for structural equivalence. Social Networks 14, 63-90.

Lorrain, F., White, H.C., 1971. Structural equivalence of individuals in social networks. Journal of Mathematical Sociology 1, 49-80.

`dist`, `hclust`, `REGE`, `crit.fun`, `opt.par`, `opt.random.par`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```#generating a simple network corresponding to the simple Sum of squares #structural equivalence with blockmodel: # null com # null null n<-20 net<-matrix(NA,ncol=n,nrow=n) clu<-rep(1:2,times=c(5,15)) tclu<-table(clu) net[clu==1,clu==1]<-rnorm(n=tclu[1]*tclu[1],mean=0,sd=1) net[clu==1,clu==2]<-rnorm(n=tclu[1]*tclu[2],mean=4,sd=1) net[clu==2,clu==1]<-rnorm(n=tclu[2]*tclu[1],mean=0,sd=1) net[clu==2,clu==2]<-rnorm(n=tclu[2]*tclu[2],mean=0,sd=1) D<-sedist(M=net) plot.mat(net, clu=cutree(hclust(d=D,method="ward"),k=2)) ```