Empirical_Degree_Distribution_ER <- function(n,lambda){

G<-sample_gnp(n,lambda/n)

D<-degree_distribution(G)

print(D[1:5])
print(dpois(0:4,lambda))

Max1<-max(abs(D-dpois(0:(length(D)-1),lambda)))

NMax<-which.max(abs(D-dpois(0:(length(D)-1),lambda)))

print(NMax)

Max2<-max(dpois(length(D):max(length(D),ceiling(lambda)),lambda))

Max<-max(Max1,Max2)

return(Max)
}


Empirical_Degree_Distribution_KM <- function(n,lambda){

D<-rpois(n,lambda)
D[n]<-D[n]+(sum(D)%%2)

G<-simplify(sample_degseq(D))

D<-degree_distribution(G)

print(D[1:5])
print(dpois(0:4,lambda))

Max1<-max(abs(D-dpois(0:(length(D)-1),lambda)))

NMax<-which.max(abs(D-dpois(0:(length(D)-1),lambda)))

print(NMax)

Max2<-max(dpois(length(D):max(length(D),ceiling(lambda)),lambda))

Max<-max(Max1,Max2)

return(Max)
}


p_pa <- function(k,m,delta){

y<- (2+delta/m)*(k>=m)*gamma(k+delta)*gamma(m+2+delta+delta/m)/(gamma(m+delta)*gamma(k+3+delta+delta/m))

return(y)
}

Empirical_Degree_Distribution_PA <- function(n,edges,delta){

G<-sample_pa(n,power=1,m=edges,zero.appeal=1+delta)

D<-degree_distribution(G)

M<-100

for(i in min(length(D),M+1):(M+1)) { D[i]=0}

print(D[1:5])
print(p_pa(0:4,edges,delta))

Max<-max(abs(D[1:(M+1)]-p_pa(0:M,edges,delta)))

NMax<-which.max(abs(D[1:(M+1)]-p_pa(0:M,edges,delta)))

print(NMax)

return(Max)
}


Empirical_Degree_Distribution_RGG <- function(n,r){

lambda<-pi*n*r^2

G<-sample_grg(n,r)

D<-degree_distribution(G)

print(D[1:5])
print(dpois(0:4,lambda))

Max1<-max(abs(D-dpois(0:(length(D)-1),lambda)))

NMax<-which.max(abs(D-dpois(0:(length(D)-1),lambda)))

print(NMax)

Max2<-max(dpois(length(D):max(length(D),ceiling(lambda)),lambda))

Max<-max(Max1,Max2)

return(Max)
}