I’m trying to code a hierarchical network using NetLogo following the paper “Hierarchical organization in complex networks” (2003) by Erzsebet Ravasz and Albert-Laszlo Barabasi. I first would like to build the model in Section II (Hierarchical Network Model) and then Section III (Hierarchical Organization in Real Networks) but struggling to find a way to implement it due to lack of Object Oriented Programming in NetLogo.

text

So far, here’s my code for Section II (Hierarchical Network Model):

globals[dist help generation-count]

turtles-own[
  center-node?
  generation
  model?
]

to setup
  ca
  set dist 1.2
   crt num[
    create-links-with other turtles
    set shape "dot"
    set size 1.5
  ]
  let c 0
  repeat (num - 1)[
    ask one-of turtles with[xcor = 0 and ycor = 0][
      set heading 360 / (num - 1) * c fd dist
    ]
    set c c + 1
  ]
  ask turtles[
    ifelse(xcor = 0 and ycor = 0)[set center-node? true][set center-node? false]
    set color red
    set generation 1
    set model? true
  ]
  set generation-count 1
 ; repeat x[recreate]
end

to recreate
  set generation-count generation-count + 1
  let c 0
  set help count turtles
  loop [
    ask turtles with[model? = true][
      hatch 1 [
        set generation generation-count
        repeat generation - 1[
          set heading 0
          set heading (heading + 360 / (num - 1) * c)
          fd generation * dist
        ]
        set model? false
      ]
    ]
    finish-member(turtles with[count link-neighbors = 0])
    set c c + 1
    ask turtles with[center-node? = false and generation = generation-count][create-links-with other turtles with[center-node? = true and generation = 1]]
    ;layout
    if(count turtles = help * num)[stop]
  ]
end

to finish-member[people]
  ask people[create-links-with other people]
end

to layout
  ;; the number 3 here is arbitrary; more repetitions slows down the
  ;; model, but too few gives poor layouts
  repeat 100 [
    ;; Refactoring the link lengths (MODIFY DENSITY HERE?)
    ;; the more turtles we have to fit into the same amount of space,
    ;; the smaller the inputs to layout-spring we'll need to use
    let factor ((sqrt count turtles) / 3) ;; Here SF-density-mod influences the distance factor across the network - will impact search function...
                                          ;; numbers here are arbitrarily chosen for pleasing appearance
    layout-spring turtles links (1 / factor) (7 / factor) (1 / factor)
    display  ;; for smooth animation
  ]
  ;;; Centering network ;;;
  ;; don't bump the edges of the world
  let x-offset max [xcor] of turtles + min [xcor] of turtles
  let y-offset max [ycor] of turtles + min [ycor] of turtles
  ;; big jumps look funny, so only adjust a little each time
  set x-offset limit-magnitude x-offset 0.1
  set y-offset limit-magnitude y-offset 0.1
  ask turtles [ setxy (xcor - x-offset / 2) (ycor - y-offset / 2) ]
end

to-report limit-magnitude [number limit]
  if number > limit [ report limit ]
  if number < (- limit) [ report (- limit) ]
  report number
end

I was unable to position them like in the paper so I resorted to the NetLogo “layout” procedure but then I realized the way they were being linked is also incorrect; the peripheral outer nodes are not correctly linking to the peripheral central nodes.

Expected
My Model

The attached picture is for when n=2, which is just incorrect.
I want to be able to somehow use recursion so I can also use it for Section III (Hierarchical Organization in Real Networks) as well.
Please help me find a solution to this.