sna (version 0.3)

sedist: Find a Matrix of Distances Between Positions Based on Structural Equivalence

Description

sedist uses the graphs indicated by g in dat to assess the extent to which each vertex is structurally equivalent; joint.analysis determines whether this analysis is simultaneous, and method determines the measure of approximate equivalence which is used.

Usage

sedist(dat, g=c(1:dim(dat)[1]), method="hamming", 
    joint.analysis=FALSE, mode="digraph", diag=FALSE, code.diss=FALSE)

Arguments

dat

A graph or graph stack

g

A vector indicating which elements of dat should be examined

method

One of ``correlation'', ``euclidean'', ``hamming'', and ``gamma''

joint.analysis

Should equivalence be assessed across all networks jointly (TRUE), or individually within each (FALSE)

mode

``digraph'' for directed data, otherwise ``graph''

diag

Boolean indicating whether diagonal entries (loops) should be treated as meaningful data

code.diss

Reverse-code the raw comparison values

Value

• A matrix of similarity/difference scores

Details

sedist provides a basic tool for assessing the (approximate) structural equivalence of actors. (Two vertices i and j are said to be structurally equivalent if i->k iff j->k for all k.) SE similarity/difference scores are computed by comparing vertex rows and columns using the measure indicated by method:

1. correlation: the product-moment correlation
2. euclidean: the euclidean distance
3. hamming: the Hamming distance
4. gamma: the gamma correlation

Once these similarities/differences are calculated, the results can be used with a clustering routine (such as equiv.clust) or an MDS (such as cmdscale).

References

Breiger, R.L.; Boorman, S.A.; and Arabie, P. (1975). ``An Algorithm for Clustering Relational Data with Applications to Social Network Analysis and Comparison with Multidimensional Scaling.'' Journal of Mathematical Psychology, 12, 328-383.

Burt, R.S. (1976). ``Positions in Networks.'' Social Forces, 55, 93-122.

Wasserman, S., and Faust, K. Social Network Analysis: Methods and Applications. Cambridge: Cambridge University Press.

See Also

equiv.clust, blockmodel

Examples

#Create a random graph with _some_ edge structure
g.p<-sapply(runif(20,0,1),rep,20)  #Create a matrix of edge 
                                   #probabilities
g<-rgraph(20,tprob=g.p)            #Draw from a Bernoulli graph 
                                   #distribution

#Get SE distances
g.se<-sedist(g)

#Plot a metric MDS of vertex positions in two dimensions
library(mva)
plot(cmdscale(as.dist(g.se)))