Draw Dyad Census-Conditioned Random Graphs
rguman generates random draws from a dyad census-conditioned uniform random graph distribution.
rguman(n, nv, mut = 0.25, asym = 0.5, null = 0.25,
method = c("probability", "exact"), return.as.edgelist = FALSE)n |
the number of graphs to generate. |
nv |
the size of the vertex set (|V(G)|) for the random graphs. |
mut |
if |
asym |
if |
null |
if |
method |
the generation method to use. |
return.as.edgelist |
logical; should the resulting graphs be returned in edgelist form? |
A simple generalization of the Erdos-Renyi 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).
A matrix or array containing the drawn adjacency matrices
The famous mathematicians referenced in this man page now have misspelled names, due to R's difficulty with accent marks.
Carter T. Butts buttsc@uci.edu
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.
#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)
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