globals
[
  color-list
  time
  degrees
  new-node
  mean-score
  av-time
]

turtles-own
[
  score
]


;;;;;;;;;;;;;;;;;;;;;;;
;;; Main Procedures ;;;
;;;;;;;;;;;;;;;;;;;;;;;

to go
  set mean-score mean [score] of turtles
  if (mean [score] of turtles = 1)
    [stop]
;  clear-last-round
  ask turtles [ update-color ]                        ;;have turtles try to find a partner
;  let partnered-turtles turtles with [ partnered? ]
;  ask partnered-turtles [ select-action ]           ;;all partnered turtles select action
  ask turtles [ get-payoff ]

  do-plotting
  tick
  set time ticks
end

to update-color 
  let newcolor color
  let numgreen count link-neighbors with [color = green]
  let numred count link-neighbors with [color = red]
  let numyellow count link-neighbors with [color = yellow]
  let numblue count link-neighbors with [color = blue]
  let minnum min (list numgreen numred numyellow numblue)
  let goodlist []
  if (numgreen <= minnum) [set goodlist fput green goodlist]
  if (numred <= minnum) [set goodlist fput red goodlist]
  if (numblue <= minnum) [set goodlist fput blue goodlist]
  if (numyellow <= minnum) [set goodlist fput yellow goodlist]
  set color one-of goodlist
end

;;layout all nodes and links
to do-layout
  repeat 5 [layout-spring turtles links 0.2 4 0.9]
  display
end


;;calculate the payoff for this round and
;;display a label with that payoff.
to get-payoff
  let mycolor color
  let sumscore 0.0
  ifelse (count link-neighbors = 0) [
    set score 1.0
  ] [
  ask link-neighbors [
    if (color != mycolor) [
      set sumscore sumscore + 1.0]
  ]
  set score (sumscore / count link-neighbors)
  ]
end


;;;;;;;;;;;;;;;;;;;;;;;;
;;; Setup Procedures ;;;
;;;;;;;;;;;;;;;;;;;;;;;;

to generate-lattice-topology

  ct
  
  create-turtles num-nodes [
      set shape "circle"
      set size int (800 / (num-nodes + 200))
    ]

  ;; setup small world topology
  set-default-shape turtles "outlined circle"
  create-lattice
  rewire-network
  
  set-random-colors
  layout-turtles
end

to generate-ba-topology
  ;; (for this model to work with NetLogo's new plotting features,
  ;; __clear-all-and-reset-ticks should be replaced with clear-all at
  ;; the beginning of your setup procedure and reset-ticks at the end
  ;; of the procedure.)
  if (any? links) [ask links [die]]
  ct
  reset-ticks
  
  set-default-shape turtles "circle"
  set degrees []   ;; initialize the array to be empty
  ;; make the initial network of two turtles and an edge
  
  make-node ;; add the very first node
  
  let first-node new-node  ;; remember that its the first node
  
  ;; the following few lines create a cycle of length 5
  ;; this is just an arbitrary way to start a network
  
  let prev-node new-node
  repeat 4 [
    make-node ;; second node
    make-edge new-node prev-node ;; make the edge
    set degrees lput prev-node degrees
    set degrees lput new-node degrees
    set prev-node new-node
  ]
  make-edge new-node first-node
  
  set time 0

  while [count turtles < num-nodes] [
    ;; new edge is green, old edges are gray
    ask links [ set color gray + 2]
    ;; old turtles are blue
    ask turtles [set color gray + 2]
  
    make-node  ;; add one new node
  
    ;; it's going to have m edges
    repeat m [
      let partner find-partner new-node      ;; find a partner for the new node
      ask partner [set color gray + 2]    ;; set color of partner to gray
      make-edge new-node partner     ;; connect it to the partner we picked before
    ]
    do-layout
  ]

  set-random-colors
end

;;set the variables that all turtles share
to set-random-colors
set color-list [ blue yellow red green]
  ask turtles [
    set score 0
       set color item ( random length color-list ) color-list
  ]
end


to layout-turtles
  
  ;; Layout turtles:
  layout-circle (sort turtles) max-pxcor - 8
  ;; space out turtles to see clustering
  ask turtles
  [
    facexy 0 0
    if who mod 2 = 0 [fd 4]
    set color item ( random length color-list ) color-list
  ]
  display
end
  
;; WARNING: the simplified rewiring algorithm does not certain checks (ie disconnected graph)
;; for large networksthis shouldn't be too much of an issue.
to rewire-network
  ask links
  [
    ;; whether to rewire it or not?
    if (random-float 1) < rewiring-probability
    [
      ask end1
      [
        create-link-with one-of other turtles with [not link-neighbor? myself ]
          [set color gray + 1.5]
      ]
      die
    ]
  ]
end


;; creates a new lattice
to create-lattice
  reset-ticks
  ;; iterate over the nodes
  let n 0
  while [n < count turtles]
  [
    ;; connect to closest neighbor
    ask turtle n [
              create-link-with
              turtle ((n + 1) mod count turtles)
              create-link-with
              turtle ((n + 2) mod count turtles)
    ]
    set n n + 1
  ]
  
end


;; connects the two nodes
to make-link-between [node1 node2]
  ask node1 [
    create-link-with node2
      [ set color gray + 1.5]
  ]
end

to vary-small-world
  let sum-times 0
  set av-time 0
  
   set-current-plot "av. time to solution"
   clear-plot
  
  set rewiring-probability 1
  while [rewiring-probability >= 0] [
    set sum-times 0

    repeat num-rep [
      set-current-plot "mean score"
      clear-plot
      generate-lattice-topology
      rewire-network
      repeat 20 [
        set-random-colors
        reset-ticks
        while [mean [score] of turtles != 1] [
          go
        ]
        set sum-times (sum-times + ticks)
      ]
    ]
    set av-time (sum-times / num-rep / 20)
     set-current-plot "av. time to solution"
     set-current-plot-pen "av-time"

     plotxy rewiring-probability av-time
     set rewiring-probability (rewiring-probability - 0.1)
  ]
end

to vary-ba-topology
  let sum-times 0
  set av-time 0
  
   set-current-plot "av. time to solution"
   clear-plot
  
  set prob-pref 1
  while [prob-pref >= 0] [
    set sum-times 0

    repeat num-rep [
      set-current-plot "mean score"
      clear-plot
      generate-ba-topology
      repeat 20 [
        set-random-colors
        reset-ticks
        while [mean [score] of turtles != 1] [
          go
        ]
        set sum-times (sum-times + ticks)
      ]
    ]
    set av-time (sum-times / num-rep / 20)
     set-current-plot "av. time to solution"
     set-current-plot-pen "av-time"

     plotxy prob-pref av-time
     set prob-pref (prob-pref - 0.1)
  ]
end

to-report find-partner [node1]
  ;; set a local variable called ispref that
  ;; determines if this link is going to be
  ;; preferential of not
  let ispref (random-float 1 <= prob-pref)
  
  ;; initialize partner to be the node itself
  ;; this will have to be changed
  let partner node1
  
  ;; if preferential attachment then choose
  ;; from our degrees array
  ;; otherwise chose one of the turtles at random
  ifelse ispref 
  [
    set partner one-of degrees
   ]
   [
     set partner one-of turtles
     ]
     
   ;; but need to check that partner chosen isn't
   ;; the node itself and also isn't a node that
   ;; our node is already connected to
   ;; if this is the case, it will try another
   ;; partner and try again
  let checkit true
  while [checkit] [
    ask partner [
      ifelse ((link-neighbor? node1) or (partner = node1))
        [
          ifelse ispref 
          [
            set partner one-of degrees
           ]
           [
             set partner one-of turtles
           ]
            set checkit true
         ]
         [
           set checkit false
         ]
       ] 
    ]
  report partner
end

;; connects the two turtles
to make-edge [node1 node2]
  ask node1 [
    ifelse (node1 = node2) 
    [
      show "error: self-loop attempted"
    ]
    [
      create-link-with node2 [ set color green ]
     ;; position the new node near its partner
      setxy ([xcor] of node2) ([ycor] of node2)
      rt random 360
      fd 8
      set degrees lput node1 degrees
     set degrees lput node2 degrees
     ]
  ]
end

to make-node
  create-turtles 1  ;; don't know what this is - lada
  [
    set color gray + 2
    set size 2
    set new-node self ;; set the new-node global
  ]
end
;;;;;;;;;;;;;;;;
;;; Plotting ;;;
;;;;;;;;;;;;;;;;

to do-plotting
     ;; plot the number of infected individuals at each step
     set-current-plot "mean score"
     set-current-plot-pen "score"
     
     let tmp mean [score] of turtles
     plotxy ticks tmp
end
@#$#@#$#@
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BUTTON
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increase prob-pref
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OBSERVER
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1

@#$#@#$#@
## HOW IT WORKS

This is a model of graph coloring. Adjacent nodes strive to have different colors. Each node's strategy is to choose the color that it observes the least in its neighborhood. This model measures how long the network takes to solve this problem (that is how long does it take until no two adjacent nodes have the same color). 

You can try this on two types of network toplogy:
1) a small world network topology
2) a growing network with a tunable preferential attachment topology

## HOW TO USE IT

First choose what kind of topology you'd like to run graph coloring on.
If you choose GENERATE-SMALL-WORLD, then you'll get a lattice where every node is connected to its two closest neighbors. A fraction REWIRE-PROBABILITY will be rewired randomly.

If you choose GENERATE-BA-TOPOLOGY, then the network will be grown such that nodes are added one at a time, each with M links. With probability PROB-PREF the attachment will be in proportion to the number of edges the existing node already has (rich-get-richer, or preferential attachment). With probability (1 - PROB-PREF), the new node will attach to an existing node at random.

Click GO-ONCE to have each node try to change color just once. Click GO (forever) to have the nodes update until they achieve a solution.

To see how the speed with which the network converges to a solution varies with the rewiring probability in the small-world network topology, use VARY-SMALL-WORLD. However, this will generate a new topology and solve the problem NUM-REP times for each rewiring probability (0,0.1,0.2,...). So you'll probably want to uncheck 'view updates' at the top so that this process goes more quickly. 

## CREDITS AND REFERENCES

This model was adapted from: Wilensky, U. (2005).  NetLogo Small Worlds model.  http://ccl.northwestern.edu/netlogo/models/SmallWorlds.  Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

Model is based on:
Michael Kearns, Siddarth Suri,Nick Montfort, An Experimental Study of the Coloring Problem on Human Subject Networks, Science 313, 824 (2006).

It was written by Lada Adamic, 2008-2012
@#$#@#$#@
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@#$#@#$#@
NetLogo 5.0.2
@#$#@#$#@
setup
repeat 5 [rewire-one]
@#$#@#$#@
@#$#@#$#@
<experiments>
  <experiment name="vary-rewiring-probability" repetitions="5" runMetricsEveryStep="false">
    <go>rewire-all</go>
    <timeLimit steps="1"/>
    <exitCondition>rewiring-probability &gt; 1</exitCondition>
    <metric>average-path-length</metric>
    <metric>clustering-coefficient</metric>
    <steppedValueSet variable="rewiring-probability" first="0" step="0.025" last="1"/>
  </experiment>
</experiments>
@#$#@#$#@
@#$#@#$#@
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