# Computes distances in terms of Structural equivalence (Lorrain and White, 1971)

### 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 |

### 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 |

`handle.interaction` |
How should the interaction between the vertices analysed be handled: |

`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 |

### 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)

Aleš Žiberna

### 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.

### See Also

`dist`

, `hclust`

, `REGE`

, `crit.fun`

, `opt.par`

, `opt.random.par`

### Examples

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))
``` |