Caveman-Solaria

Caveman-Solaria preview image

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Tags

complex networks 

Tagged by Marcello Tomasini about 10 years ago

networks 

Tagged by Marcello Tomasini about 10 years ago

small world 

Tagged by Marcello Tomasini about 10 years ago

Model group BioComplex Lab | Visible to everyone | Changeable by group members (BioComplex Lab)
Model was written in NetLogo 5.1.0 • Viewed 511 times • Downloaded 29 times • Run 0 times
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;;;;;;;;;;;;;;;;;;;;;;;;;;
;;;; Setup Procedures ;;;;
;;;;;;;;;;;;;;;;;;;;;;;;;;

to setup
  clear-all
  set-default-shape turtles "circle"
  create-initial-substrate 
  reset-ticks
end 

to create-initial-substrate
  create-turtles number_of_nodes
  ask turtles
  [ 
    set color red
    facexy 0 0
    set size 3
  ]
  let n 0
  while [n < number_of_nodes]
  [
    make-edge turtle n
              turtle ((n + 1) mod count turtles)
    set n n + 1
  ]
  layout-circle (sort turtles) max-pxcor - 5
end 

;;;;;;;;;;;;;;;;;;;;;;;;
;;;; Main Procedure ;;;;
;;;;;;;;;;;;;;;;;;;;;;;;

to go
  let terminate False
  ;; 1 - fix a vertex i
  ;; ask iterate once over all turtles in random order
  ask turtles
  [ 
    ;; 2 - for every other vertex j compute Rij according to equation:
    ;;            1                     if mij >= k
    ;; (mij/k)^alfa * (1 - p) + p       if k > mij > 0
    ;;            p                     if mij = 0
    ;; where mij is the number of vertices that are adjacient both to i and j
    ;; with the additional constraint that Rij = 0 if i and j are already connected
    let Rij n-values (number_of_nodes)[0]
    let others [who] of other turtles
    foreach others
    [
      ; if it is a neighbor of i we already set Rij to 0
      if not link-neighbor? turtle ?
      [ 
        ;; Get the number of vertices that are adjacent both to i and j
        ; neighbors of i
        let i_neighbors link-neighbors
        ; neigbors of j
        let j_neighbors [link-neighbors] of turtle ?
        let mij 0
        foreach [who] of i_neighbors 
        [
          if member? ? ([who] of j_neighbors) [ set mij (mij + 1) ]
        ]
        ; ? variable referes to current item in others list. 
        ; Since others list is a list of turtle IDs I can use ? as an index in Rij list.
        if mij >= k
        [
          set Rij replace-item ? Rij 1
        ]
        if mij < k and mij > 0
        [
          set Rij replace-item ? Rij ( (mij / k) ^ alfa * (1 - p) + p )
        ]
        if mij = 0
        [
          set Rij replace-item ? Rij p
        ]
      ];; END_if
    ];; END_foreach     
    
    ;; 3 - Sum Rij over all j, and normalize each to obtain variables Pij = Rij / Sum_l!=i Ril.
    ;; Then since Sum_j Pij = 1, we can interpret Pij as the probability that i will connect to j.
    ;; Furthermore, we can interpret Pij geometrically as follows: divide the unit interval (0,1)
    ;; into n - 1 half-open subintervals with length Pij for all j != i.
    let sum_of_Rij sum Rij
    let Pij map [? / ifelse-value (sum_of_Rij > 0) [sum_of_Rij] [1] ] Rij
    
    ;; 4 - A uniform random variable r is then generated on (0,1). 
    ;; it must fall into one of the subintervals, corresponding to j*
    let j* (jstar others Pij)
    ;; 5 - Connect i to j*
    if j* != -1
    [
      make-edge turtle who
                turtle j*
    ]

    ;; Stop when reach this threshold
    if count links >= (k * number_of_nodes / 2)
    [ 
      set terminate True 
      stop ; exit ask turtles
    ]
  ];; END_ask turtles
  if terminate [ stop ]
  tick
end 

to-report jstar [others Pij]
  let r random-float 1
  while [ r = 0 ] [ set r random-float 1 ] ; random-float might includes 0, even though it is unlikely
  let partial-sum 0
  foreach others
  [
    set partial-sum partial-sum + (item ? Pij)
    if partial-sum > r ; it is the same as if r > partial-sum and r < (partial-sum + (item ? Pij))
    [
      report ?
    ] 
  ]
  report -1
end 

;;;;;;;;;;;;;;;;;;;;;;;;;
;;;; Link Procedures ;;;;
;;;;;;;;;;;;;;;;;;;;;;;;;

;; connects the two turtles

to make-edge [node1 node2]
  ask node1 [ 
    create-link-with node2  [ set color blue ] 
  ]
end 

to relayout
  ; layout-spring turtle-set link-set spring-constant spring-length repulsion-constant
  layout-spring turtles links 0.2 25 5
end 

There is only one version of this model, created about 10 years ago by Marcello Tomasini.

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