globals
[ 
  average-degree
  clustering-coefficient
  turns
  nb-links
]


breed [ links link ]
breed [ nodes node ]

nodes-own[
  degree
  node-clustering-coefficient
  pred
  valeur
]

links-own[
strength
]
;;;;;;;;;;;;;;;;;;;;;;;;
;;; Setup Procedures ;;;
;;;;;;;;;;;;;;;;;;;;;;;;

to setup
  ca
  create-custom-nodes nb-nodes[
    fd 40
    set shape "circle"
    ]
  social-network
  set turns 0
end

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

to go
  set turns turns + 1
  social-network
  
  let tmp []
  ask nodes [set tmp lput degree tmp]
  set average-degree (sum tmp) / nb-nodes
  
  set-current-plot "degree distribution"
  if (max tmp != 0 ) [
    set-histogram-num-bars max tmp
    set-plot-x-range 0 max tmp
  histogram-list tmp]
  
    ;; find the clustering coefficient and add to the aggregate for all iterations
  find-clustering-coefficient
  set nb-links count links
end

;------------------
;-- managing the decaying and destroying of links (the evolution but creation)
;-- cf the paper "Structure of growing social networks" (Emily M. Jin, Michelle Girvan, and M. E. J. Newman)
;-------------------
to social-network
  let N 0
  ;-- step one
  let np nb-nodes * ( nb-nodes - 1) / 2
  ;if (np > nb-nodes) [set np nb-nodes]
  ask n-of (np * r0) nodes [
     make-edge self one-of remove self values-from nodes[self]
     ] 
  
  ;-- step tow
  let degree-list []
  ask nodes [set degree-list lput (degree * (degree - 1)) degree-list]
  let nm (sum degree-list ) / 2
  set N (nm * r1)
  ;if (N > count nodes with [degree >= 2]) [set N count nodes with [degree >= 2]]
  let i 0
  let max-nb-duo ((max degree-list) * ((max degree-list) - 1))
  while [i < N] [
    ask one-of nodes with [degree >= 2] [
     if ((degree * (degree - 1)) >= random max-nb-duo) [
       let neighbor1 one-of __link-neighbors
       let neighbor2 nobody
       while [neighbor1 = neighbor2 or neighbor2 = nobody]  [set neighbor2 one-of __link-neighbors]
       make-edge neighbor1 neighbor2
     ]
     set i i + 1
   ]
   ]
   
   ;-- step three
   set degree-list []
   ask nodes [set degree-list lput degree degree-list]
   let max-degree max degree-list
   let ne (sum degree-list) / 2
   set i 0
   while [i < ne * gamma] [
     ask one-of nodes [
       if (degree > random max-degree) [
         ask one-of __my-links [destroy-link]
       ]
     set i i + 1
     ]
   ]
   
   ;--step four decay links
   ;this step is optional but I think it gives better results
   ask links [set strength strength - 0.01
     if (strength < 0) [destroy-link]]

end

;------------------------------------
;; connects the two nodes
;------------------------------------
to make-edge [node1 node2]
  without-interruption [
  ask node1 [
    ifelse (member? node2 __link-neighbors) [
      ask __link-with node2 [set strength 1]
    ][
    if (the-degree node1 < Z and the-degree node2 < Z ) [
      __create-link-with node2 [ 
        set color green
        set strength 1
        ]
      set degree degree + 1
      ask node2 [set degree degree + 1]
      ]
    ]
  ]
  ]
end
;------------------------------------
;; destroy a link
;------------------------------------
to destroy-link
  ask __end1 [set degree degree - 1]
  ask __end2 [set degree degree - 1]
  die
end

to-report the-degree [vertice]
let tmp 0
  ask vertice [ set tmp count __link-neighbors]
report tmp
end

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;; Clustering computations ;;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

to-report in-neighborhood? [ hood ]
  report ( member? __end1 hood and member? __end2 hood )
end


to find-clustering-coefficient
  ifelse not any? nodes with [count __link-neighbors > 1]
  [
    set clustering-coefficient 0
  ]
  [
    let total 0
    ask nodes with [ count __link-neighbors <= 1]
      [ set node-clustering-coefficient "undefined" ]
    ask nodes with [ count __link-neighbors > 1]
    [
      let hood __link-neighbors
      set node-clustering-coefficient (2 * count links with [ in-neighborhood? hood ] / 
                                         ((count hood) * (count hood - 1)) )
      ;; find the sum for the value at nodes
      set total total + node-clustering-coefficient
    ]
    ;; take the average
    set clustering-coefficient total / count nodes with [count __link-neighbors > 1]
  ]
end


;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;; graph dispaly the software graphviz can is built to represent graph and can be dowload from ATT labs          ;;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
to print-dot-file
file-open "LN.dot"
file-print "graph \" learning network \" { graph [epsilon=0.15]; node [shape=point];" 
ask links [file-print "\""+ value-from __end1[who] + "\"--\"" + value-from __end2[who] + "\""]
file-print "}"
file-close
end

to dijkstra [node1]
 locals [fa us p]
 set fa []
 
  ask nodes [
    set color white
    set valeur nb-nodes + 1
    set pred nobody ]

 set us node1
 set valeur-of us 0
 set fa lput us fa
 
 while [not empty? fa] [
   set us first fa
   set fa remove us fa
   ask us [
     set color red
     ask __link-neighbors [
       set p valeur-of us + strength-of __link-with us
       if (p < valeur) [
         set pred us
         set valeur p ]
       if (not member? self fa and color = white) [
         set fa lput self fa
         set color yellow
         ]
       ]
     ]
     ]
end

to short-path [node1 node2]
  let path []
  let link-path []
  dijkstra node1
  let s node2
    while [pred-of s != nobody and s != node1] [
      set path lput s path
      ask s [
        set color-of __link-with pred yellow
        set link-path lput __link-with pred link-path
        ]
      set s pred-of s
      ]
      set path lput node1 path
end
@#$#@#$#@
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Command Center
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setup
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go
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degree distribution
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turns
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MONITOR
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NIL
nb-links
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1

@#$#@#$#@
WHAT IS IT?
-----------
In some networks, a few "hubs" have lots of connections, while everybody else only has a few.  This model shows one way such networks can arise.

Such networks can be found in a surprisingly large range of real world situations, ranging from the connections between websites to the collaborations between actors.

This model generates these networks by a process of "preferential attachment", in which new network members prefer to make a connection to the more popular existing members.


HOW IT WORKS
------------
The model starts with two nodes connected by an edge.

At each step, a new node is added.  A new node picks an existing node to connect to randomly, but with some bias.  More specifically, a node's chance of being selected is directly proportional to the number of connections it already has, or its "degree." This is the mechanism which is called "preferential attachment."


HOW TO USE IT
-------------
Pressing the GO ONCE button adds one new node.  To continuously add nodes, press GO.

The LAYOUT? switch controls whether or not the layout procedure is run.  This procedure attempts to move the nodes around to make the structure of the network easier to see.

The PLOT? switch turns off the plots which speeds up the model.

The RESIZE-NODES button will make all of the nodes take on a size representative of their degree distribution.  If you press it again the nodes will return to equal size.

If you want the model to run faster, you can turn off the LAYOUT? and PLOT? switches and/or freeze the view (using the on/off button in the control strip over the view). The LAYOUT? switch has the greatest effect on the speed of the model.

If you have LAYOUT? switched off, and then want the network to have a more appealing layout, press the REDO-LAYOUT button which will run the layout-step procedure until you press the button again. You can press REDO-LAYOUT at any time even if you had LAYOUT? switched on and it will try to make the network easier to see.

THINGS TO NOTICE
----------------
The networks that result from running this model are often called "scale-free" or "power law" networks. These are networks in which the distribution of the number of connections of each node is not a normal distribution -- instead it follows what is a called a power law distribution.  Power law distributions are different from normal distributions in that they do not have a peak at the average, and they are more likely to contain extreme values (see Barabasi 2002 for a further description of the frequency and significance of scale-free networks).  Barabasi originally described this mechanism for creating networks, but there are other mechanisms of creating scale-free networks and so the networks created by the mechanism implemented in this model are referred to as Barabasi scale-free networks.

You can see the degree distribution of the network in this model by looking at the plots. The top plot is a histogram of the degree of each node.  The bottom plot shows the same data, but both axes are on a logarithmic scale.  When degree distribution follows a power law, it appears as a straight line on the log-log plot.  One simple way to think about power laws is that if there is one node with a degree distribution of 1000, then there will be ten nodes with a degree distribution of 100, and 100 nodes with a degree distribution of 10.


THINGS TO TRY
-------------
Let the model run a little while.  How many nodes are "hubs", that is, have many connections?  How many have only a few?  Does some low degree node ever become a hub?  How often?

Turn off the LAYOUT? switch and freeze the view to speed up the model, then allow a large network to form.  What is the shape of the histogram in the top plot?  What do you see in log-log plot? Notice that the log-log plot is only a straight line for a limited range of values.  Why is this?  Does the degree to which the log-log plot resembles a straight line grow as you add more node to the network?


EXTENDING THE MODEL
-------------------
Assign an additional attribute to each node.  Make the probability of attachment depend on this new attribute as well as on degree.  (A bias slider could control how much the attribute influences the decision.)

Can the layout algorithm be improved?  Perhaps nodes from different hubs could repel each other more strongly than nodes from the same hub, in order to encourage the hubs to be physically separate in the layout.


NETWORK CONCEPTS
----------------
There are many ways to graphically display networks.  This model uses a common "spring" method where the movement of a node at each time step is the net result of "spring" forces that pulls connected nodes together and repulsion forces that push all the nodes away from each other.  This code is in the layout-step procedure. You can force this code to execute any time by pressing the REDO LAYOUT button, and pressing it again when you are happy with the layout.


NETLOGO FEATURES
----------------
Both nodes and edges are turtles.  Edge turtles have the "line" shape.  The edge turtle's SIZE variable is used to make the edge be the right length.

Lists are used heavily in this model.  Each node maintains a list of its neighboring nodes.


RELATED MODELS
--------------
See other models in the Networks section of the Models Library, such as Giant Component.

See also Network Example, in the Code Examples section.


CREDITS AND REFERENCES
----------------------
This model is based on:
Albert-Laszlo Barabasi. Linked: The New Science of Networks, Perseus Publishing, Cambridge, Massachusetts, pages 79-92.

For a more technical treatment, see:
Albert-Laszlo Barabasi & Reka Albert. Emergence of Scaling in Random Networks, Science, Vol 286, Issue 5439, 15 October 1999, pages 509-512.

Barabasi's webpage has additional information at: http://www.nd.edu/~alb/

The layout algorithm is based on the Fruchterman-Reingold layout algorithm.  More information about this algorithm can be obtained at: http://citeseer.ist.psu.edu/fruchterman91graph.html.

For a model similar to the one described in the first extension, please consult:
W. Brian Arthur, "Urban Systems and Historical Path-Dependence", Chapt. 4 in Urban systems and Infrastructure, J. Ausubel and R. Herman (eds.), National Academy of Sciences, Washington, D.C., 1988.

To refer to this model in academic publications, please use:  Wilensky, U. (2005).  NetLogo Preferential Attachment model.  http://ccl.northwestern.edu/netlogo/models/PreferentialAttachment.  Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

In other publications, please use:  Copyright 2005 Uri Wilensky.  All rights reserved.  See http://ccl.northwestern.edu/netlogo/models/PreferentialAttachment for terms of use.
@#$#@#$#@
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@#$#@#$#@
NetLogo 3.1.3
@#$#@#$#@
set layout? false
setup repeat 175 [ go ]
repeat 35 [ layout ]
@#$#@#$#@
@#$#@#$#@
@#$#@#$#@