centralgraph: Find the Central Graph of a Labeled Graph Set
Description
Returns the central graph of a set of labeled graphs, i.e. that graph in which i->j iff i->j in >=50% of the graphs within the set. If normalize==TRUE, then the value of the i,jth edge is given as the proportion of graphs in which i->j.
Usage
centralgraph(dat, normalize=FALSE)
Arguments
dat
Data array to be analyzed. By assumption, the first dimension of the array indexes the graph, with the next two indexing the actors.
normalize
Boolean indicating whether the results should be normalized. The result of this is the "mean matrix". By default, normalize==FALSE.
Value
A matrix containing the central graph (or mean matrix)
Details
The central graph of a set of graphs S is that graph C which minimizes the sum of Hamming distances between C and G in S. As such, it turns out (for the dichotomous case, at least), to be analogous to both the mean and median for sets of graphs. The central graph is useful in a variety of contexts; see the references below for more details.
References
Banks, D.L., and Carley, K.M. (1994). ``Metric Inference for Social Networks.'' Journal of Classification.''
[object Object],[object Object]
0.5 is used as the cutoff value regardless of whether or not the data is dichotomous (as is tacitly assumed). The routine is unaffected by data type when normalize==TRUE.
#Generate some random graphs
dat<-rgraph(10,5)
#Find the central graph
cg<-centralgraph(dat)
#Plot the central graph
gplot(cg)
#Now, look at the mean matrix
cg<-centralgraph(dat,normalize=TRUE)
print(cg)network