Is this a correct way to create an igraph object?

I am trying to generate a random network with preferential attachment. Here is the code:


get_random_integer = function(value) {
  result = floor(runif(1, min=1, max=value))

  return (result)

get_random_link = function(m, value) {
  links = to_vector(m)
  maxVal = length(links) + 1
  result = floor(runif(1, min=1, max=maxVal))

  return (links[result])

to_vector = function(listVar) {

  return (unlist(listVar, use.names=FALSE))

set_initial_edges = function() {
  loop = rep(1:4, each = 2)
  vertices = c(loop[-1], loop[1])

  return (vertices)

create_graph_data = function(start, end, gamma) {
  l = list()
  m = list(1,2,3,4)

  for (i in seq(start,end)) {
    p = rbernoulli(1, p = gamma)

    if (p) {
      x = get_random_integer(i)
    } else {
      x = get_random_link(m, i)

    l = append(list(i,x), l)
    m = append(list(x), m)

  data = to_vector(l)

  return (data)

generate_graph = function(end) {
  gamma = 0.5   # the probability of choosing a link at random among all the pages
  initial_vertices = 4   # the number of vertices of the initial graph
  initial_edges = set_initial_edges()   # the edges of the initial graph
  start = initial_vertices + 1    # the starting value of the interval
  increment = end - start + 1   # the number of vertices to add to the initial graph
  data = create_graph_data(start, end, gamma)   # creates an edge for each                     additional vertex

    grph <- make_empty_graph() %>%          # initialize an empty graph
      add_vertices(initial_vertices) %>%    # add the first 4 vertices
      add_edges(initial_edges) %>%          # add the first 4 edges
      add_vertices(increment) %>%           # add to the initial graph the remaining vertices
      add_edges(data)                       # add to the initial graph the remaining edges 

    return (grph)

  a = generate_graph(10000)


I know this is not the most straightforward way, I should have probably used an adjacency matrix, but anyway…

every object is created as follows, see the second-to-last line of the code above:

       a = generate_graph(10000)

where the parameter, 10000, is the number of nodes to be added to the graph.

I was able to do almost anything with such graphs, but I have encountered a problem: if I use igraph methods like transitivity or vertex_connectivity, the result is always zero, regardless of the dimension size of the graph.
Is this happening because of a property of the model I am building, or the way I am building the igraph objects is wrong?

Many thanks