tda1=function(M,B,be,gammat)
## M = number of nodes of the graph
## B = number of Monte Carlo replicates
## be = beta parameter of the Mittag-Leffler distribution (0 < be <= 1)
## gammat = scale factor (parameter of the exponential distribution if beta is 1)
{
tda=rep(0,B)

for (b in 1:B)
{
 A=matrix(rep(0,M^2),nrow=M)
 c=0
 t=0

 while (c==0)
 {
  tau <- rexp(1) 
  if (be < 1) 
  {
   u <- runif(1)
   w <- sin(be*pi)/tan(be*pi*u) - cos(be*pi)
   tau <- tau* (w^(1/be))
  }
  tau <- gammat * tau
  deltat=tau

  i=sample(1:M, 2, replace = FALSE)
  if (A[i[1],i[2]]==0)
  {
   A[i[1],i[2]]=1
   A[i[2],i[1]]=1
   t=t+deltat
   for (j in 1:M)
   {
    if ((j!=i[1])&(j!=i[2]))
    {
     if (A[i[1],j]*A[i[2],j]==1) {c=1}
    }
   }
  } 
  else
  {
   A[i[1],i[2]]=0
   A[i[2],i[1]]=0
   t=t+deltat
  }
 }
tda[b]=t
}
tda1=tda
}


######################################
## First experiment

M=10
B=10000
gammat <- 1

tda90=tda1(M,B,0.90,1)
tda95=tda1(M,B,0.95,1)
tda98=tda1(M,B,0.98,1)
tda99=tda1(M,B,0.99,1)

tdatot=c(tda90,tda95,tda98,tda99)
beta=c(rep(0.90,B),rep(0.95,B),rep(0.98,B),rep(0.99,B))
boxplot(tdatot ~ beta,main="First example (Triangles)",xlab="beta",ylab="time",sub="M=10 nodes")
by(tdatot,beta,summary)


######################################
## Second experiment

B=10000
be <- 0.99 
gammat <- 1


mtda=matrix(rep(0,10*B),ncol=10)
Mlab=5*(1:10)
for (M in (1:10))
{
  mtda[,M]=tda1(5*M,B,be,gammat)
}

boxplot(mtda,names=Mlab,main="First example (Triangles)",xlab="number of nodes",ylab="time",sub="beta=0.99")
mtda_mean=mean(as.data.frame(mtda))
mtda_med=rep(0,10)
for (M in 1:10)
{
  mtda_med[M]=median(mtda[,M])
}

grange=range(mtda_mean,mtda_med)
plot(Mlab,mtda_med,type="o",col="blue",main="First example (Triangles)",xlab="number of nodes",ylab="time",sub="beta=0.99",ylim=grange)
lines(Mlab,mtda_mean, type="o", pch=22, lty=2, col="red")
legend(5, grange[2], c("median","mean"), cex=1, col=c("blue","red"), pch=21:22, lty=1:2)