Assignment_8

Network Statistics (Marriages between characters in the Game of Thrones Novels).

Inferential Stats

Looking at a 1,000 random networks, transitivity has a random chance to produce a value greater than the observed value, on all three factors (size, edges, dyads), especially when considering the number of nodes.

cug.t<-function(cug.object){
  (cug.object$obs.stat-mean(cug.object$rep.stat))/sd(cug.object$rep.stat)
}

cugtransSize<-cug.test(gotmarr.mat,FUN=gtrans,mode="graph",cmode="size")
cugtransSize

Univariate Conditional Uniform Graph Test

Conditioning Method: size 
Graph Type: graph 
Diagonal Used: FALSE 
Replications: 1000 

Observed Value: 0.3787375 
Pr(X>=Obs): 0.99 
Pr(X<=Obs): 0.01 

cugtransEdges<-cug.test(gotmarr.mat,FUN=gtrans,mode="graph",cmode="edges")
cugtransEdges

Univariate Conditional Uniform Graph Test

Conditioning Method: edges 
Graph Type: graph 
Diagonal Used: FALSE 
Replications: 1000 

Observed Value: 0.3787375 
Pr(X>=Obs): 0.066 
Pr(X<=Obs): 0.934 

cugtransDyad<-cug.test(gotmarr.mat,FUN=gtrans,mode="graph",cmode="dyad.census")
cugtransDyad

Univariate Conditional Uniform Graph Test

Conditioning Method: dyad.census 
Graph Type: graph 
Diagonal Used: FALSE 
Replications: 1000 

Observed Value: 0.3787375 
Pr(X>=Obs): 0.061 
Pr(X<=Obs): 0.939 

cug.t(cugtransSize)

[1] -2.424939

cug.t(cugtransEdges)

[1] 1.473769

cug.t(cugtransDyad)

[1] 1.473727

par(mfrow=c(1,3))
plot(cugtransSize, main="Transitivity \nConditioned on Size" )
plot(cugtransEdges, main="Transitivity \nConditioned on Edges" )
plot(cugtransDyad, main="Transitivity \nConditioned on Dyads" )

par(mfrow=c(1,1))

Looking at a 1,000 random networks, betweenness has a random chance to produce a value greater than the observed value when compared to the properties edges and dyads. However, the property size was unable to generate a value higher than the observed betweenness score.

cug.t<-function(cug.object){
  (cug.object$obs.stat-mean(cug.object$rep.stat))/sd(cug.object$rep.stat)
}

cugbetSize<-cug.test(gotmarr.mat,FUN=centralization, FUN.arg=list(FUN=betweenness, cmode="undirected"), mode="graph",cmode="size")
cugbetSize

Univariate Conditional Uniform Graph Test

Conditioning Method: size 
Graph Type: graph 
Diagonal Used: FALSE 
Replications: 1000 

Observed Value: 0.2765138 
Pr(X>=Obs): 0 
Pr(X<=Obs): 1 

cugbetEdges<-cug.test(gotmarr.mat,FUN=centralization, FUN.arg=list(FUN=betweenness, cmode="undirected"), mode="graph",cmode="edges")
cugbetEdges

Univariate Conditional Uniform Graph Test

Conditioning Method: edges 
Graph Type: graph 
Diagonal Used: FALSE 
Replications: 1000 

Observed Value: 0.2765138 
Pr(X>=Obs): 0 
Pr(X<=Obs): 1 

cugbetDyad<-cug.test(gotmarr.mat,FUN=centralization, FUN.arg=list(FUN=betweenness, cmode="undirected"), mode="graph",cmode="dyad")
cugbetDyad

Univariate Conditional Uniform Graph Test

Conditioning Method: dyad.census 
Graph Type: graph 
Diagonal Used: FALSE 
Replications: 1000 

Observed Value: 0.2765138 
Pr(X>=Obs): 0 
Pr(X<=Obs): 1 

cug.t(cugbetSize)

[1] 12.00625

cug.t(cugbetEdges)

[1] 4.697649

cug.t(cugbetDyad)

[1] 4.76025

par(mfrow=c(1,3))
plot(cugbetSize, main="Betweenness \nConditioned on Size" )
plot(cugbetEdges, main="Betweenness \nConditioned on Edges" )
plot(cugbetDyad, main="Betweenness \nConditioned on Dyads" )

par(mfrow=c(1,1))