rguman {sna}R Documentation

Draw Dyad Census-Conditioned Random Graphs

Description

rguman generates random draws from a dyad census-conditioned uniform random graph distribution.

Usage

rguman(n, nv, mut = 0.25, asym = 0.5, null = 0.25, 
    method = c("probability", "exact"))

Arguments

n the number of graphs to generate.
nv the size of the vertex set (|V(G)|) for the random graphs.
mut if method=="probability", the probability of obtaining a mutual dyad; otherwise, the number of mutual dyads.
asym if method=="probability", the probability of obtaining an asymmetric dyad; otherwise, the number of asymmetric dyads.
null if method=="probability", the probability of obtaining a null dyad; otherwise, the number of null dyads.
method the generation method to use. "probability" results in a multinomial dyad distribution (conditional on the underlying rates), while "exact" results in a uniform draw conditional on the exact dyad distribution.

Details

A simple generalization of the Erd"{o}s-R'{e}nyi family, the U|MAN distributions are uniform on the set of graphs, conditional on order (size) and the dyad census. As with the E-R case, there are two U|MAN variants. The first (corresponding to method=="probability") takes dyad states as independent multinomials with parameters m (for mutuals), a (for asymmetrics), and n (for nulls). The resulting pmf is then

p(G=g|m,a,n) = (M+A+N)!/(M!A!N!) m^M a^A n^N,

where M, A, and N are realized counts of mutual, asymmetric, and null dyads, respectively. (See dyad.census for an explication of dyad types.)

The second U|MAN variant is selected by method=="exact", and places equal mass on all graphs having the specified (exact) dyad census. The corresponding pmf is

p(G=g|M,A,N) = M!A!N!/(M+A+N)!.

U|MAN graphs provide a natural baseline model for networks which are constrained by size, density, and reciprocity. In this way, they provide a bridge between edgewise models (e.g., the E-R family) and models with higher order dependence (e.g., the Markov graphs).

Value

A matrix or array containing the drawn adjacency matrices

Author(s)

Carter T. Butts buttsc@uci.edu

References

Holland, P.W. and Leinhardt, S. (1976). ``Local Structure in Social Networks.'' In D. Heise (Ed.), Sociological Methodology, pp 1-45. San Francisco: Jossey-Bass.

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

See Also

rgraph, rgnm, dyad.census

Examples

#Show some examples of extreme U|MAN graphs
gplot(rguman(1,10,mut=45,asym=0,null=0,method="exact")) #Clique
gplot(rguman(1,10,mut=0,asym=45,null=0,method="exact")) #Tournament
gplot(rguman(1,10,mut=0,asym=0,null=45,method="exact")) #Empty

#Draw a sample of multinomial U|MAN graphs
g<-rguman(5,10,mut=0.15,asym=0.05,null=0.8)

#Examine the dyad census
dyad.census(g)

[Package sna version 1.5 Index]