Problem in a generation of a random number with sample and rbinom in R

In my R code, while I generate a number with sample (1: edge_counter, 1) everything works fine but while I generate it with rbinom (1, i, p) the code doesn't work. What could be the problem?

Here is the code where i generate a graph following the Forrest Fire module, the random generation problem is when i generate a random x:

install.packages("igraph")

library(igraph)

par(mar=c(1,1,1,1))

#Number of node to add in the graph
num_nodes = 10

#Forward burning probability
p = 0.37

#Backward burning ratio
r = 0.32

#Parameters for the plot 
node_count <- rep(0, times = num_nodes)
edge_count <- rep(0, times = num_nodes)

g1 <- make_empty_graph(1)

for(i in 2:num_nodes)
{
  exit = 0
  visited_node <- rep(FALSE, times = i)
  g1 = add_vertices(g1,1)
  
  #orphans extention
  q = runif(1,0,1)
  if(q > 0.2)
  {   
    #chose an ambassador node 
    w <- sample(1:(vcount(g1)-1), 1)
  
    # connecting the ambassador with the node
    v = i; 
    g1 = add_edges(g1,c(v,w))
  
    # count number of node linked to the ambassador 
    edge_counter <- 0 
    for(h in 1: i)
    {
      if(g1[w, h] == 1 || g1[h, w] == 1)
      {
        edge_counter =  edge_counter + 1
      }
    }
    
    selected_node <- rep(FALSE, times = i)
   
    while(exit == 0)
    {
      x = sample(1:edge_counter, 1)
      #x = rbinom(1, i, p)

        # select x links incident to w choosing from among both out links and in links  
        j = 0
        while(j != x)
        {
          prob <- runif(1,0,1)
          random_node <- sample(1:i, 1) 
            
          if(selected_node[random_node] == FALSE)
          {
            #chose out-link
            if(prob < r) 
            {
              if(g1[w, random_node] == 1)
              {
                selected_node[random_node] = TRUE 
                j = j+1
              }
            }
            #chose in-link
            else 
            {
              if (g1[random_node, w] == 1) 
              {
                selected_node[random_node] = TRUE
                j = j+1
              }
            }
          }
        } 
        
        #v forms out-links to w1,...wx
        for(l in 1:i)
        {
          if((selected_node[l] == TRUE) && (l != v))
          {
            g1 = add_edges(g1,c(v,l))
          }
        }
        
        old_v <- v
        
        visited_node[v] = TRUE
        
        for(j in 1:i)
        {
          if ((selected_node[j] == TRUE) && (visited_node[v] == FALSE))
          {
            v <- j
            break
          }
        }
        
        if(old_v == v)
        {
          exit = 1  
        }
      }
    }
  
  #Node and edge count
  node_count[i] = gorder(g1)
  edge_count[i] = gsize(g1)
}

# number of nodes respect number of edges 
plot(node_count, edge_count, xlab = "Number of nodes", ylab = "Number of edges")

#graph plot 
plot(g1)