Inferential Network Statistics

A closer look into the S&P 500 stock network properties.

This is the same network that I used for Hw 7. The small network above is a filtered correlation network created from the S&P 500. I grabbed the close prices from all s&p 500 stocks for 2021. I then created a correlation matrix from those prices. I then created ties for stocks that were 98% correlated. This filtered down the list of 500 stocks to 32 stocks. I then filtered out any isolates.

CUG-tests to Test Network Properties

I first need to change my network objects into adjacency matrixs.

small.mat <- as.matrix(as_adjacency_matrix(small_network))



small.cug <- sna::cug.test(small.mat,FUN=gtrans,mode="digraph",cmode="size", reps = 100)


small.cug

Univariate Conditional Uniform Graph Test

Conditioning Method: size 
Graph Type: digraph 
Diagonal Used: FALSE 
Replications: 100 

Observed Value: 0.4322034 
Pr(X>=Obs): 1 
Pr(X<=Obs): 0 

plot(small.cug)

paste("The T stat: ",(small.cug$obs.stat-mean(small.cug$rep.stat))/sd(small.cug$rep.stat))

[1] "The T stat:  -4.09960327592022"

There is a low probability the transitivity can be randomly generated.

Creating T stat funciton

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

Cug test to different Network Properties

Degree

small.cug <-cug.test(small.mat,FUN=centralization,  FUN.arg=list(FUN=degree, cmode="indegree"), mode="digraph", cmode="size") 
#plot vs simulation results
plot(small.cug)

paste("T Statistic: ",cug.t(small.cug))

[1] "T Statistic:  -1.03322042697641"

There is a good probability that the degree could be randomly generated.

Betweenness

small.bet <-cug.test(small.mat,FUN=centralization,  FUN.arg=list(FUN=betweenness, cmode="directed"), mode="digraph", cmode="size", reps=100) 
#plot vs simulation results
plot(small.bet)

paste("T stat: ", cug.t(small.bet))

[1] "T stat:  37.733590672985"

There is a very small probability that the betweeness could be randomly generated.

Transitivity

small.trans <- cug.test(small.mat,FUN=gtrans,mode="digraph",cmode="dyad")
small.trans

Univariate Conditional Uniform Graph Test

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

Observed Value: 0.4322034 
Pr(X>=Obs): 0 
Pr(X<=Obs): 1 

plot(small.trans)

paste("T stat: ", cug.t(small.trans))

[1] "T stat:  7.6129532301842"

Edges

small.edge<-cug.test(small.mat,FUN=gtrans,mode="digraph",cmode="edges", reps=100)
small.edge

Univariate Conditional Uniform Graph Test

Conditioning Method: edges 
Graph Type: digraph 
Diagonal Used: FALSE 
Replications: 100 

Observed Value: 0.4322034 
Pr(X>=Obs): 0 
Pr(X<=Obs): 1 

plot(small.edge)

paste("T stat: ", cug.t(small.edge))

[1] "T stat:  16.395883128983"