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######################################################################
#
# randomgraph.R
#
# copyright (c) 2004, Carter T. Butts <buttsc@uci.edu>
# Last Modified 02/28/24
# Licensed under the GNU General Public License version 2 (June, 1991)
# or later.
#
# Part of the R/sna package
#
# This file contains various routines for random graph generation in
# R.
#
# Contents:
# rewire.ud
# rewire.ws
# rgbn
# rgmn
# rgnmix
# rgraph
# rguman
# rgws
#
######################################################################
#rewire.ud - Perform a uniform dyadic rewiring of a graph or graph stack
rewire.ud<-function(g,p,return.as.edgelist=FALSE){
#Pre-process the raw input
g<-as.sociomatrix.sna(g)
if(is.list(g))
return(lapply(g,rewire.ud,p=p))
#End pre-processing
#Coerce g to an array
if(length(dim(g))==2)
g<-array(g,dim=c(1,NROW(g),NCOL(g)))
n<-dim(g)[1]
nv<-dim(g)[2]
#Perform the rewiring, and return the result
rewired<-.C("udrewire_R",g=as.double(g),as.double(n),as.double(nv), as.double(p),PACKAGE="sna")
if(!return.as.edgelist)
array(rewired$g,dim=c(n,nv,nv))
else
as.edgelist.sna(array(rewired$g,dim=c(n,nv,nv)))
}
#rewire.ws - Perform a Watts-Strogatz rewiring of a graph or graph stack
rewire.ws<-function(g,p,return.as.edgelist=FALSE){
#Pre-process the raw input
g<-as.sociomatrix.sna(g)
if(is.list(g))
return(lapply(g,rewire.ud,p=p))
#End pre-processing
#Coerce g to an array
if(length(dim(g))==2)
gi<-array(g,dim=c(1,NROW(g),NCOL(g)))
go<-gi
n<-dim(gi)[1]
nv<-dim(gi)[2]
#Perform the rewiring, and return the result
rewired<-.C("wsrewire_R",as.double(gi),go=as.double(go),as.double(n), as.double(nv),as.double(p),PACKAGE="sna")
if(!return.as.edgelist)
array(rewired$go,dim=c(n,nv,nv))
else
as.edgelist.sna(array(rewired$go,dim=c(n,nv,nv)))
}
#rgbn - Draw from a biased net model
rgbn<-function(n, nv, param=list(pi=0, sigma=0, rho=0, d=0.5, delta=0, epsilon=0), burn=nv*nv*5*1e2, thin=nv*nv*5, maxiter=1e7, method=c("mcmc","cftp"), dichotomize.sib.effects=FALSE, return.as.edgelist=FALSE, seed.graph=NULL, max.density=1){
#Allocate memory for the graphs (and initialize)
g<-array(0,dim=c(n,nv,nv))
if(!is.null(seed.graph)){
seed.graph<-as.sociomatrix.sna(seed.graph)
if(length(dim(seed.graph))>2)
g[1,,]<-seed.graph[1,,]
else
g[1,,]<-seed.graph
}
#Get the parameter vector
p<-rep(0,4)
if(!is.null(param$pi))
p[1]<-param$pi[1]
if(!is.null(param$sigma))
p[2]<-param$sigma[1]
if(!is.null(param$rho))
p[3]<-param$rho[1]
if(!is.null(param$delta))
p[4]<-param$delta[1]
if((p[4]>0)&&(match.arg(method)=="cftp"))
stop("Satiation parameter (delta) not supported with CFTP at present; use MCMC instead.\n")
if(!is.null(param$d)){ #Base event rates (convert to nv x nv form)
d<-matrix(param$d,nv,nv)
}else
d<-matrix(0,nv,nv)
if(!is.null(param$epsilon)){ #Inhibition events (in aggregate) - convert to nv x nv form
if(any(param$epsilon>0)&&(match.arg(method)=="cftp")){
stop("Inhibition events (epsilon) not supported with CFTP at present; use MCMC instead.\n")
}
e<-matrix(param$epsilon,nv,nv)
}else{ #Not using, by default
e<-matrix(0,nv,nv)
}
#Take the draws
early.termination<-FALSE #Flag for early termination
if(match.arg(method)=="mcmc"){
sim<-.C("bn_mcmc_R",g=as.integer(g),as.double(nv),as.double(n), as.double(burn),as.integer(thin),as.double(p[1]),as.double(p[2]),as.double(p[3]),as.double(d), as.double(p[4]),as.double(e),as.integer(dichotomize.sib.effects), dm=as.double(max.density*nv*(nv-1)),PACKAGE="sna")
g<-array(sim$g,dim=c(n,nv,nv))
early.termination<-sim$dm<0 #Make sure we didn't stop early
}else{
if(any(d>0)){ #If d==0, just return empty graphs
if(all(d==1)){ #If d==1, just return complete graphs (no delta support yet!)
for(i in 1:n){
g[i,,]<-1
diag(g[i,,])<-0
}
}else{ #OK, a nontrivial case. Let's go for it.
d[d==0]<-1e-10 #CFTP algorithm not so happy with 0s
d[d==1]<-1-1e-10 #Doesn't like exact 1s, either
for(i in 1:n){
g[i,,]<-matrix(.C("bn_cftp_R",g=as.integer(g[i,,]),as.integer(nv), as.double(p[1]),as.double(p[2]),as.double(p[3]),as.double(d), as.integer(maxiter),as.integer(dichotomize.sib.effects),PACKAGE="sna",NAOK=TRUE)$g,nv,nv)
}
}
}
}
#Return the result
if(return.as.edgelist)
out<-as.edgelist.sna(g)
else{
if(dim(g)[1]==1)
out<-g[1,,]
else
out<-g
}
if(early.termination) #Mark the output as tainted if necessary
attr(out,"early.termination")<-TRUE
out
}
#r[i]=1-u^i
#p r[1]^(n-1)
#p^2 (n-1)C1 (1-r[1]) r[2]^(n-2)
#p^3 (n-1)C2 (1-r[1])(1-r[2]) r[3]^(n-3)
#...
#p^i (n-1)C(i-1) r[i]^(n-i) prod_j=1^{i-1} (1-r[j])
# = p^i (n-1)C(i-1) (1-u^i)^(n-i) u^{i(i-1)/2}
#rgmn - Draw a density-conditioned graph
rgnm<-function(n,nv,m,mode="digraph",diag=FALSE,return.as.edgelist=FALSE){
#Allocate the graph stack and related things
g<-vector(mode="list",n)
nv<-rep(nv,length=n)
m<-rep(m,length=n)
#Create the graphs
for(i in 1:n){
if(nv[i]==0){ #Degenerate null graph
if(m[i]>0)
stop("Too many edges requested in rgnm.")
else{
mat<-matrix(nrow=0,ncol=3)
attr(mat,"n")<-0
}
g[[i]]<-mat
}else if(nv[i]==1){ #Isolate (perhaps w/loop)
if(m[i]>diag)
stop("Too many edges requested in rgnm.")
if(m[i]==1){
mat<-matrix(c(1,1,1),nrow=1,ncol=3)
attr(mat,"n")<-1
}else{
mat<-matrix(nrow=0,ncol=3)
attr(mat,"n")<-1
}
g[[i]]<-mat
}else if(m[i]==0){ #Empty graph
mat<-matrix(nrow=0,ncol=3)
attr(mat,"n")<-nv[i]
g[[i]]<-mat
}else{ #Everything else
if(mode=="digraph"){
if(diag){ #Digraph w/loops
if(m[i]>nv[i]^2)
stop("Too many edges requested in rgnm.")
j<-sample(nv[i]^2,m[i])
r<-((j-1)%%nv[i])+1
c<-((j-1)%/%nv[i])+1
mat<-cbind(r,c,rep(1,m[i]))
}else{ #Digraph, no loops
if(m[i]>nv[i]*(nv[i]-1))
stop("Too many edges requested in rgnm.")
j<-sample(nv[i]*(nv[i]-1),m[i])
c<-((j-1)%/%(nv[i]-1))+1
r<-(((j-1)%%(nv[i]-1))+1)+((((j-1)%%(nv[i]-1))+1)>(c-1))
mat<-cbind(r,c,rep(1,m[i]))
}
}else if(mode=="graph"){
if(diag){ #Unirected graph, w/loops
if(m[i]>nv[i]*(nv[i]+1)/2)
stop("Too many edges requested in rgnm.")
j<-sample(nv[i]*(nv[i]+1)/2,m[i])
c<-nv[i]-floor(sqrt(1/4+2*(nv[i]*(nv[i]+1)/2-j))-1/2)
r<-j+nv[i]-c*(nv[i]+1)+c*(c+1)/2
mat<-cbind(r,c,rep(1,m[i]))
mat<-rbind(mat,cbind(c,r,rep(1,m[i])))
}else{ #Undirected graph, no loops
if(m[i]>nv[i]*(nv[i]-1)/2)
stop("Too many edges requested in rgnm.")
j<-sample(nv[i]*(nv[i]-1)/2,m[i])
c<-nv[i]-1-floor(sqrt(1/4+2*(choose(nv[i],2)-j))-1/2)
r<-j-(c-1)*nv[i]+c*(c-1)/2+c
mat<-cbind(r,c,rep(1,m[i]))
mat<-rbind(mat,cbind(c,r,rep(1,m[i])))
}
}else
stop("Unsupported mode in rgnm.")
attr(mat,"n")<-nv[i] #Set graph size
g[[i]]<-mat
}
}
#Return the results
if(!return.as.edgelist)
as.sociomatrix.sna(g)
else{
if(n>1)
g
else
g[[1]]
}
}
#Simple function to produce graphs with fixed exact or expected mixing
#matrices. n should be the number of desired graphs, tv a vector of types,
#and mix a mixing matrix whose rows and columns correspond to the entries of
#tv. If method==probability, mix[i,j] should contain the probability of
#an edge from a vertex of type i to one of type j; otherwise, mix[i,j] should
#contain the number of ties from vertices of type i to those of type j in
#the resulting graph.
rgnmix<-function (n, tv, mix, mode="digraph", diag=FALSE, method=c("probability", "exact"), return.as.edgelist=FALSE)
{
if(match.arg(method)=="probability"){ #If method==probability, call rgraph
return(rgraph(n=length(tv),m=n,tprob=mix[tv,tv],mode=mode,diag=diag,return.as.edgelist=return.as.edgelist))
}else{ #Otherwise, use the exact method
g<-array(0,dim=c(n,length(tv),length(tv)))
if(is.character(tv)){
if(is.null(rownames(mix)))
stop("Vertex types may only be given as characters for mixing matrices with applicable rownames.\n")
tv<-match(tv,rownames(mix))
}
tcounts<-tabulate(tv,NROW(mix))
if(mode=="graph"){
for(i in 1:n){
for(j in 1:NROW(mix)) #Row types
if(tcounts[j]>0){ # (ignore if none of type j)
for(k in j:NROW(mix)) #Col types
if(tcounts[k]>0){ # (ignore if none of type k)
if(j==k){ #Diagonal case
if(tcounts[j]==1){ # Single entry
if(diag)
g[i,tv==j,tv==k]<-mix[j,k]
}else if((tcounts[j]==2)&&(!diag)){ # Stupid hack for rgnm bug
if(mix[j,k])
g[i,tv==j,tv==k]<-rbind(c(0,1),c(1,0))
}else{ # Multiple entries
g[i,tv==j,tv==k]<-rgnm(n=1,nv=tcounts[j],m=mix[j,k], mode="graph",diag=diag)
}
}else{ #Off-diagonal case
g[i,tv==j,tv==k][sample(1:(tcounts[j]*tcounts[k]),mix[j,k], replace=FALSE)]<-1
}
}
}
g[i,,]<-g[i,,]|t(g[i,,]) #Symmetrize
}
}else{
for(i in 1:n){
for(j in 1:NROW(mix)) #Row types
if(tcounts[j]>0){ # (ignore if none of type j)
for(k in 1:NROW(mix)) #Col types
if(tcounts[k]>0){ # (ignore if none of type k)
if(j==k){ #Diagonal case
if(tcounts[j]==1){ # Single entry
if(diag)
g[i,tv==j,tv==k]<-mix[j,k]
}else{ # Multiple entries
g[i,tv==j,tv==k]<-rgnm(n=1,nv=tcounts[j],m=mix[j,k], mode="digraph",diag=diag)
}
}else{ #Off-diagonal case
g[i,tv==j,tv==k][sample(1:(tcounts[j]*tcounts[k]),mix[j,k], replace=FALSE)]<-1
}
}
}
}
}
}
#Return the result
if (n==1)
g<-g[1,,]
if(return.as.edgelist)
as.edgelist.sna(g)
else
g
}
#rgraph - Draw a Bernoulli graph.
rgraph<-function(n,m=1,tprob=0.5,mode="digraph",diag=FALSE,replace=FALSE,tielist=NULL,return.as.edgelist=FALSE){
if(is.null(tielist)){ #Draw using true Bernoulli methods
g<-list()
directed<-(mode=="digraph")
if(length(dim(tprob))>3)
stop("tprob must be a single element, vector, matrix, or 3-d array.")
if(length(dim(tprob))==3){
pmode<-3
if((dim(tprob)[1]!=m)||(dim(tprob)[2]!=n)||(dim(tprob)[3]!=n))
stop("Incorrect tprob dimensions.")
}else if(length(dim(tprob))==2){
pmode<-3
if((dim(tprob)[1]!=n)||(dim(tprob)[2]!=n))
stop("Incorrect tprob dimensions.")
}else{
pmode<-0
tprob<-rep(tprob,length=m)
}
for(i in 1:m){
if(length(dim(tprob))==3)
g[[i]]<-.Call("rgbern_R",n,tprob[i,,],directed,diag,pmode,PACKAGE="sna")
else if(length(dim(tprob))==2)
g[[i]]<-.Call("rgbern_R",n,tprob,directed,diag,pmode,PACKAGE="sna")
else
g[[i]]<-.Call("rgbern_R",n,tprob[i],directed,diag,pmode,PACKAGE="sna")
}
#Return the result
if(return.as.edgelist){
if(m==1)
g[[1]]
else
g
}else
as.sociomatrix.sna(g)
}else{ #Draw using edge value resampling
g<-array(dim=c(m,n,n))
if(length(dim(tielist))==3){
for(i in 1:m)
g[i,,]<-array(sample(as.vector(tielist[i,,]),n*n,replace=replace), dim=c(n,n))
}else{
for(i in 1:m)
g[i,,]<-array(sample(as.vector(tielist),n*n,replace=replace),dim=c(n,n))
}
if(!diag)
for(i in 1:m)
diag(g[i,,])<-0
if(mode!="digraph")
for(i in 1:m){
temp<-g[i,,]
temp[upper.tri(temp)]<-t(temp)[upper.tri(temp)]
g[i,,]<-temp
}
#Return the result
if(!return.as.edgelist){
if(m==1)
g[1,,]
else
g
}else
as.edgelist.sna(g)
}
}
#rguman - Draw from the U|MAN graph distribution
rguman<-function(n,nv,mut=0.25,asym=0.5,null=0.25,method=c("probability","exact"),return.as.edgelist=FALSE){
#Create the output structure
g<-array(0,dim=c(n,nv,nv))
#Create the dyad list
dl<-matrix(1:(nv^2),nv,nv)
dlu<-dl[upper.tri(dl)]
dll<-t(dl)[upper.tri(dl)]
ndl<-length(dlu) #Number of dyads
#Perform a reality check
if((match.arg(method)=="exact")&&(mut+asym+null!=ndl))
stop("Sum of dyad counts must equal number of dyads for method==exact.\n")
else if((match.arg(method)=="probability")&&(mut+asym+null!=1)){
s<-mut+asym+null
mut<-mut/s; asym<-asym/s; null<-null/s
}
#Draw the graphs
for(i in 1:n){
#Determine the number of dyads in each class
if(match.arg(method)=="probability"){
mc<-rbinom(1,ndl,mut)
ac<-rbinom(1,ndl-mc,asym/(asym+null))
nc<-ndl-mc-ac
}else{
mc<-mut
ac<-asym
nc<-null
}
#Draw the dyad states
ds<-sample(rep(1:3,times=c(mc,ac,nc)))
#Place edges accordingly
if(mc>0){
g[i,,][dlu[ds==1]]<-1 #Mutuals
g[i,,][dll[ds==1]]<-1
}
if(ac>0){
g[i,,][dlu[ds==2]]<-rbinom(ac,1,0.5) #Asymetrics
g[i,,][dll[ds==2]]<-1-g[i,,][dlu[ds==2]]
}
}
#Return the result
if(return.as.edgelist)
as.edgelist.sna(g)
else{
if(n>1)
g
else
g[1,,]
}
}
#rgws - Draw a graph from the Watts-Strogatz model
rgws<-function(n,nv,d,z,p,return.as.edgelist=FALSE){
#Begin by creating the lattice
tnv<-nv^d
temp<-vector()
nums<-1:nv
count<-tnv/nv
for(i in 1:d){
temp<-cbind(temp,rep(nums,count))
nums<-rep(nums,each=nv)
count<-count/nv
}
lat<-as.matrix(dist(temp,method="manhattan"))<=z #Identify nearest neighbors
diag(lat)<-0
#Create n copies of the lattice
if(n>1)
lat<-apply(lat,c(1,2),rep,n)
else
lat<-array(lat,dim=c(1,tnv,tnv))
#Rewire the copies
g<-lat
lat<-array(.C("wsrewire_R",as.double(lat),g=as.double(g),as.double(n), as.double(tnv),as.double(p),PACKAGE="sna")$g,dim=c(n,tnv,tnv))
#Return the result
if(return.as.edgelist)
as.edgelist.sna(lat)
else{
if(n>1)
lat
else
lat[1,,]
}
}
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