brainwaver (version 1.6)

sim.graph: Simulation of graphs

Description

Simulates four different types of graphs, random, lattice, scale-free and random with a given degree distribution.

Usage

sim.rand(n.nodes, n.edges)
sim.equadist(degree)
sim.reg(n.nodes, n.edges)

Arguments

n.nodes

number of nodes of the simulated graph

n.edges

number of edges of the simulated graph

degree

degree distribution of the simulated graph. Only for the sim.equadist function.

Value

A matrix containing the adjacency matrix of the simulated graph.

Details

The simulation of a graph with a given degree distribution is not always possible. Sometimes the random choice of the connected nodes will cause an impossible construction of the wanted graph with a given number of nodes and edges, because we do not allow to connect a node to itself. Becareful with this function and check always if the returned graph have the exact number of edges!

Examples

#Coordinates of the nodes of the graph

set2<-array(c(5,6.5,7,6.5,5,3.5,3,3.5,1,1.5,3,4.5,5,4.5,3,1.5),dim=c(8,2))
names<-c(1:8)


# For a random graph

mat<-sim.rand(8,20)

plot(set2[,1], set2[,2], type = "n",xlab="", ylab="",cex.lab=1.5)
text(set2[,1], set2[,2], names, cex = 1.5)

for(k in 2:8){
                for(q in 1:(k-1)){

                if(mat[k,q]==1)
                {

                visu <- "red"
                lines(c(set2[k,1], set2[q,1]), c(set2[k,2], set2[q,2]), col = visu)
        }

}
}

# For a lattice graph

mat<-sim.reg(8,20)

plot(set2[,1], set2[,2], type = "n",xlab="", ylab="",cex.lab=1.5)
text(set2[,1], set2[,2], names, cex = 1.5)

for(k in 2:8){
                for(q in 1:(k-1)){

                if(mat[k,q]==1)
                {

                visu <- "red"
                lines(c(set2[k,1], set2[q,1]), c(set2[k,2], set2[q,2]), col = visu)
        }

}
}

# For a graph with a given degree distribution

degree<-c(1,2,3,4,5,6,7,8)
mat<-sim.equadist(degree)

plot(set2[,1], set2[,2], type = "n",xlab="", ylab="",cex.lab=1.5)
text(set2[,1], set2[,2], names, cex = 1)

for(k in 2:8){
                for(q in 1:(k-1)){

                if(mat[k,q]==1)
                {

                visu <- "red"
                lines(c(set2[k,1], set2[q,1]), c(set2[k,2], set2[q,2]), col = visu)
        }

}
}

# For a scale-free graph

# Simulation of a scale-free degree distribution

x<-1:50
probx<-x^(-1.4)
n.nodes<-8
n.edges<-25
sf.degree<-rep(0,n.nodes)

stop<-0

while(stop==0){

r<-sample(x,n.nodes,prob=probx,replace=TRUE)
if(sum(r)==n.edges) stop<-1
  }

sf.degree<-r

mat<-sim.equadist(sf.degree)

plot(set2[,1], set2[,2], type = "n",xlab="", ylab="",cex.lab=1.5)
text(set2[,1], set2[,2], names, cex = 1)

for(k in 2:8){
                for(q in 1:(k-1)){

                if(mat[k,q]==1)
                {

                visu <- "red"
                lines(c(set2[k,1], set2[q,1]), c(set2[k,2], set2[q,2]), col = visu)
        }

}
}