sna (version 0.41)

gtrans: Compute the Transitivity of an Input Graph or Graph Stack

Description

gtrans returns the transitivity of the elements of dat selected by g, using the definition of measure. Triads involving missing values are omitted from the analysis.

Usage

gtrans(dat, g=NULL, diag=FALSE, mode="digraph", measure = c("weak", 
    "strong", "weakcensus", "strongcensus"))

Arguments

dat

A graph or graph stack

g

A vector indicating the graphs which are to be analyzed; by default, all graphs are analyzed

diag

A boolean indicating whether or not diagonal entries (loops) are to be taken as valid data

mode

"digraph" if directed triads are sought, or else "graph"

measure

One of "weak" (default), "strong", "weakcensus", or "strongcensus"

Value

• A vector of transitivity scores

Details

Transitivity is a triadic, algebraic structural constraint. In its weak form, the transitive constraint corresponds to $a \rightarrow b \rightarrow c \Rightarrow a \rightarrow c$. In the corresponding strong form, the constraint is $a \rightarrow b \rightarrow c \Leftrightarrow a \rightarrow c$. (Note that the weak form is that most commonly employed.) Where measure=="weak", the fraction of potentially intransitive triads obeying the weak condition is returned. With the measure=="weakcensus" setting, by contrast, the total number of transitive triads is computed. The strong versions of the measures are similar to the above, save in that the set of all triads is considered (since all are ``at risk'' for intransitivity).

References

Holland, P.W., and Leinhardt, S. (1972). ``Some Evidence on the Transitivity of Positive Interpersonal Sentiment.'' American Journal of Sociology, 72, 1205-1209.

Wasserman, S., and Faust, K. (1994). Social Network Analysis: Methods and Applications. Cambridge: Cambridge University Press.

See Also

triad.classify, cugtest

Examples

#Draw some random graphs
g<-rgraph(5,10)

#Find transitivity scores
gtrans(g)