P value to permutation in igraph

Question

I need to compare my value coming from a matrix bootstrap, with the original unique value, but I don't know exactly how to do this for my data. Here I have the example data

in order I need do:

1. measuring the targeted variable on the original network and save it.
2. Shuffling my original data (correlation matrix) - randomly (100x) create the graph measuring the targeted variable for this random network.
3. Save this data end of the loop Comparing the distribution of the random targeted variable with the original one saved at the begging.
4. Then if the original data is outside of the 95% of the distribution of the random variable, this mean that it's significative (the random is different of the original variable).

    library(igraph)
    ###DADOSEXEMPLO##
    valores <- c(1, 5, 3, 8, 2, 9, 3, 2, 3 ,2, 5, 3, 6, 5, 1, 5, 3, 4, 2, 2, 5, 6, 5, 7, 1, 2, 
                 8, 12, 5, 1, 5, 3, 6, 5, 9, 3,3,4,5,7,8,2,7,8,4,3,1,4,4 ) matrixnet <- matrix(valores, 7, 7) matcor <- cor(matrixnet, method = "spearman")
    
    cor_pequena <- 0.1
    matcor[] <- ifelse(matcor < cor_pequena, 0, matcor)
    matrixnetwork = graph.adjacency(matcor, mode = "undirected", 
                                    weighted = TRUE, 
                                    add.colnames = NULL, diag = FALSE)
    degree(matrixnetwork)
    #> [1] 3 4 3 3 1 2 2

    plot(matrixnetwork)

Here I calculate the unique value for the graph, in this case for the measure betw:

centr_betw(matrixnetwork, directed = FALSE, normalized = TRUE)$res

Here I apply the permutation "change value in vertices" in conjunction with the specific function I want to apply, in this case betw

set.seed(123) 
bootcentr_Betw <- lapply(seq_len(Nperm), function(x){
randomnet <- rewire(matrixnetwork, with=each_edge(0.5)) #rewire vertices with constant probability E(randomnet)$weight <- sample(E(matrixnetwork)$weight) #shuffle initial weights and assign them randomly to edges return(centr_betw(randomnet)$res) }) 

Now I need to compare the original value with the bootstrap of the randomized graph.

Below I tried to plot the original unique value against bootstrap, replicating the code I got from elsewhere

orig <- centr_betw(matrixnetwork, directed = FALSE, 
   normalized = TRUE)$res

Nperm <- 1e2
set.seed(123)
bootcentr_Betw <- replicate(Nperm, {
  randomnet <- rewire(matrixnetwork, with = each_edge(0.5))
  E(randomnet)$weight <- sample(E(matrixnetwork)$weight)
  centr_betw(randomnet)$res
})

op <- par(mfrow = c(2, 4))
for(k in seq_along(orig)) {
  main <- sprintf("Vértice: %d", k)
  bootcentr_Betw[k,] |> density() |> plot(main = main, sub = "Observed vs. randomized")
  abline(v = orig[k], col = "red")
}
par(op)

After that I tried to replicate the statistics I found here on the forum, but it didn't work. I need one p value for compare my observed value And my random network. Similar a permutation test i try this form…

# pval_eq <- numeric(length(orig))
# pval_gt <- numeric(length(orig))
# pval_le <- numeric(length(orig))
for(k in seq_along(orig)) {
  rand <- bootcentr_Betw[k, ]
  obs <- orig[k]
  pval_eq[k] <- t.test(rand, mu = obs)$p.value
  # pval_gt[k] <- t.test(rand, mu = obs, alternative = "greater")$p.value
  # pval_le[k] <- t.test(rand, mu = obs, alternative = "less")$p.value
}
setNames(
  pval_eq,
  # pval_gt,
  # pval_le,
  seq_along(orig)
)
#>             1             2             3             4             5 
#>  2.786037e-57 1.458862e-210  6.921656e-01 6.997004e-225  9.001682e-87 
#>             6             7 
#> 9.445648e-114  9.104672e-38

I try this form too, but my cod is fail.

#5. Estime o valor P (signific?ncia)

  significance=matrix(nrow=nrow(bootstrength),ncol=7)
  row.names(significance)=row.names(bootstrength)  
  colnames(significance)=c("p (rand <= obs)", "p (rand >= obs)", "p 
  (rand=obs)")

  signif.sup=function(x) sum(x>=x[1])/length(x)
  signif.inf=function(x) sum(x<=x[1])/length(x)
  signif.two=function(x) ifelse(min(x)*2>1,1,min(x)*2)

 significance[,1]=apply(bootstrength,1,signif.inf)
 significance[,2]=apply(bootstrength,1,signif.sup)
 significance[,3]=apply(significance[,-3],1,signif.two)

I basically need compare my value observed to permutation value, I thinks permutation test a good way for this. Similar code above