sna (version 2.8)

blockmodel: Generate Blockmodels Based on Partitions of Network Positions

Description

Given a set of equivalence classes (in the form of an equiv.clust object, hclust object, or membership vector) and one or more graphs, blockmodel will form a blockmodel of the input graph(s) based on the classes in question, using the specified block content type.

Usage

blockmodel(dat, ec, k=NULL, h=NULL, block.content="density", 
    plabels=NULL, glabels=NULL, rlabels=NULL, mode="digraph", 
    diag=FALSE)

Value

An object of class blockmodel.

Arguments

dat

one or more input graphs.

ec

equivalence classes, in the form of an object of class equiv.clust or hclust, or a membership vector.

k

the number of classes to form (using cutree).

h

the height at which to split classes (using cutree).

block.content

string indicating block content type (see below).

plabels

a vector of labels to be applied to the individual nodes.

glabels

a vector of labels to be applied to the graphs being modeled.

rlabels

a vector of labels to be applied to the (reduced) roles.

mode

a string indicating whether we are dealing with graphs or digraphs.

diag

a boolean indicating whether loops are permitted.

Author

Carter T. Butts

Details

Unless a vector of classes is specified, blockmodel forms its eponymous models by using cutree to cut an equivalence clustering in the fashion specified by k and h. After forming clusters (roles), the input graphs are reordered and blockmodel reduction is applied. Currently supported reductions are:

1. density: block density, computed as the mean value of the block

2. meanrowsum: mean row sums for the block

3. meancolsum: mean column sums for the block

4. sum: total block sum

5. median: median block value

6. min: minimum block value

7. max: maximum block value

8. types: semi-intelligent coding of blocks by ``type.'' Currently recognized types are (in order of precedence) ``NA'' (i.e., blocks with no valid data), ``null'' (i.e., all values equal to zero), ``complete'' (i.e., all values equal to 1), ``1 covered'' (i.e., all rows/cols contain a 1), ``1 row-covered'' (i.e., all rows contain a 1), ``1 col-covered'' (i.e., all cols contain a 1), and ``other'' (i.e., none of the above).

Density or median-based reductions are probably the most interpretable for most conventional analyses, though type-based reduction can be useful in examining certain equivalence class hypotheses (e.g., 1 covered and null blocks can be used to infer regular equivalence classes). Once a given reduction is performed, the model can be analyzed and/or expansion can be used to generate new graphs based on the inferred role structure.

References

Doreian, P.; Batagelj, V.; and Ferligoj, A. (2005). Generalized Blockmodeling. Cambridge: Cambridge University Press.

White, H.C.; Boorman, S.A.; and Breiger, R.L. (1976). ``Social Structure from Multiple Networks I: Blockmodels of Roles and Positions.'' American Journal of Sociology, 81, 730-779.

See Also

equiv.clust, blockmodel.expand

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

#Cluster based on structural equivalence
eq<-equiv.clust(g)

#Form a blockmodel with distance relaxation of 10
b<-blockmodel(g,eq,h=10)
plot(b)                            #Plot it