extensions [network] turtles-own [ ;; this is used to mark turtles we have already visited explored? ] globals [ component-size ;; number of turtles explored so far in the current component giant-component-size ;; number of turtles in the giant component giant-start-node ;; node from where we started exploring the giant component ] ;;;;;;;;;;;;;;;;;;;;;;;; ;;; Setup Procedures ;;; ;;;;;;;;;;;;;;;;;;;;;;;; to make-turtles crt num-nodes [ set xcor random-xcor set ycor random-ycor ] end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;; Network wiring procedures ;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; to all-random ca let thiswho 0 RESET-TICKS if (not any? turtles) [make-turtles] ask turtles [ set shape "circle" set size 2 ] ifelse prob-or-num? [ ask turtles [ set thiswho who ask other turtles with [who > thiswho] [ if (random-float 1 < prob-link) [ create-link-with myself ] ] ] ] [ repeat (floor (num-neighbors * num-nodes / 2)) [ ask one-of turtles [ ask one-of other turtles with [not link-neighbor? myself] [ create-link-with myself ] ] ] ] find-all-components color-giant-component set-current-plot "degree distribution" set-plot-x-range 0 (max [count link-neighbors] of turtles) set-current-plot "degree dist (log-log)" set-plot-x-range 0 precision (log ((max [count link-neighbors] of turtles) + 1) 10) 2 tick end ;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;; Network Exploration ;;; ;;; code by Uri Wilensky ;; ;;;;;;;;;;;;;;;;;;;;;;;;;;; ;; to find all the connected components in the network, their sizes and starting turtles to find-all-components set giant-component-size 0 ask turtles [ set explored? false ] ;; keep exploring till all turtles get explored loop [ ;; pick a node that has not yet been explored let start one-of turtles with [ not explored? ] if start = nobody [ stop ] ;; reset the number of turtles found to 0 ;; this variable is updated each time we explore an ;; unexplored node. set component-size 0 ;; at this stage, we recolor everything to light gray ask start [ explore (gray + 2) ] ;; the explore procedure updates the component-size variable. ;; so check, have we found a new giant component? if component-size > giant-component-size [ set giant-component-size component-size set giant-start-node start ] ] end ;; Finds all turtles reachable from this node (and recolors them) to explore [new-color] ;; node procedure if explored? [ stop ] set explored? true set component-size component-size + 1 ;; color the node set color new-color ask link-neighbors [ explore new-color ] end ;; color the giant component red to color-giant-component ask turtles [ set explored? false ] ask giant-start-node [ explore red ] ask links [ set color [color] of end1 ] ;; recolor all edges end ;;;;;;;;;;;;;;;;;;;;;;; ;;; Edge Operations ;;; ;;;;;;;;;;;;;;;;;;;;;;; ;; pick a random missing edge and create it to add-edge let node1 one-of turtles let node2 one-of turtles ask node1 [ ifelse link-neighbor? node2 or node1 = node2 ;; if there's already an edge there, then go back ;; and pick new turtles [ add-edge ] ;; else, go ahead and make it [ create-link-with node2 ] ] end ;;;;;;;;;;;;;; ;;; Layout ;;; ;;;;;;;;;;;;;; to layout ;; the number 10 here is arbitrary; more repetitions slows down the ;; model, but too few gives poor layouts repeat 10 [ do-layout display ;; so we get smooth animation ] end to do-layout layout-spring (turtles with [any? link-neighbors]) links spring-constant spring-length repulsion-strength end ; Original Copyright 2005 Uri Wilensky. ; Modified by Lada Adamic ; See Info tab for full copyright and license. @#$#@#$#@ GRAPHICS-WINDOW 328 10 718 421 45 45 4.18 1 10 1 1 1 0 0 0 1 -45 45 -45 45 0 0 1 ticks 30.0 BUTTON 210 147 312 180 redo layout do-layout T 1 T OBSERVER NIL NIL NIL NIL 1 SLIDER 5 12 177 45 num-nodes num-nodes 0 1000 505 5 1 NIL HORIZONTAL BUTTON 5 105 113 138 Erdos-Renyi all-random NIL 1 T OBSERVER NIL NIL NIL NIL 1 SLIDER 115 104 287 137 prob-link prob-link 0 0.05 0.013 0.001 1 NIL HORIZONTAL SLIDER 211 200 327 233 spring-constant spring-constant 0 2 0.2 0.1 1 NIL HORIZONTAL SLIDER 212 273 327 306 spring-length spring-length 0 20 6 1 1 NIL HORIZONTAL SLIDER 212 237 327 270 repulsion-strength repulsion-strength 0 5 0.2 0.2 1 NIL HORIZONTAL TEXTBOX 213 182 363 200 layout options 11 0.0 1 MONITOR 180 12 239 57 GC size giant-component-size 0 1 11 MONITOR 242 12 299 57 av. deg 2 * (count links) / (count turtles) 2 1 11 SWITCH 2 62 150 95 prob-or-num? prob-or-num? 0 1 -1000 SLIDER 151 62 323 95 num-neighbors num-neighbors 0 10 2 1 1 NIL HORIZONTAL PLOT 7 145 207 295 degree distribution # neighbors # of nodes 0.0 10.0 0.0 10.0 true false "" "" PENS "pen-0" 1.0 0 -14835848 false "" "histogram [count link-neighbors] of turtles" "pen-1" 1.0 1 -5298144 false "" "histogram [count link-neighbors] of turtles" PLOT 8 299 208 449 degree dist (log-log) log(degree) log(# of nodes) 0.0 0.3 0.0 0.3 true false "" "" PENS "default" 0.1 2 -16777216 true "" ";;code by Uri Wilensky\nif (not any? turtles) [stop]\nlet max-degree max [count link-neighbors] of turtles\n;; for this plot, the axes are logarithmic, so we can't\n;; use \"histogram-from\"; we have to plot the points\n;; ourselves one at a time\nplot-pen-reset ;; erase what we plotted before\n;; the way we create the network there is never a zero degree node,\n;; so start plotting at degree one\nlet degree 1\nwhile [degree <= max-degree] [\n let matches turtles with [count link-neighbors = degree]\n if any? matches\n [ plotxy log degree 10\n log (count matches) 10 ]\n set degree degree + 1\n]" @#$#@#$#@ ## WHAT IS IT? You can generate networks using several different models, starting with the Erdös-Renyi (the "randomest") network model, and a few variations. ## HOW IT WORKS All except for the GROWTH model start with a fixed number of nodes (detemined by the NUM-NODES). Then edges are added, but just how depends on the model you choose. ## HOW TO USE IT The NUM-NODES Click on LAYOUT to use a spring layout algorithm to reposition the nodes (you will typically want to keep this off while applying the network construction algorithms). With the NUM-NODES slider you determine the number of nodes in the network. The GC SIZE monitor box updates with the size of the largest component. The AV. DEG monitor box reports on the average degree in the network. The following are the network construction algorithms: ERDÖS-RENYI constructs a random graph by adding an edge between each pair of nodes with probability PROB-LINK. INTRODUCTION similar to ERDÖS-RENYI, however, random edges are added only with probability (1 - PROB-INTRO). The rest of the time the nodes try to get one of their friends to introduce them to someone they know. STATIC-GEO randomly places nodes on a 2-D square area. Each node tries to connect to its NUM-NEIGHBORS closest neighbors. This means that some nodes end up with more neighbors, because they are the closest choice to some other node even though they already have plenty of closer neighbors. GROWTH starts out with (NUM-NEIGHBORS + 1) nodes forming a fully connected clique. After this, nodes are added one by one and connected to (NUM-NEIGHBORS/2) previously added nodes (with some randomness so that one ends up with approximately the correct average degree for the entire graph when NUM-NEIGHBORS is odd. RAND-ENCOUNTER places nodes randomly on a 2D square area. They move around randomly until they occupy the same "patch" as another node, at which point they connect. REDO LAYOUT will repeatedly apply a spring-layout algorithm to the network. In the long run this can make your computer run hot, so remember to switch it off if you have NetLogo running and are not actively using it. There are also several parameters that you can adjust so that sparse networks get pulled together more tightly, but dense networks are spread out. ## THINGS TO NOTICE Try looking at how evenly the edges are distributed among the nodes in the different models. Are some nodes better connected than others? How does this come about. How many closed traids do you see in each network? Which models promote closed triads and in which are they rare? Can you explain why? ## THINGS TO TRY Try varying the density of the network. How is the size of the giant component affected? Is the transition gradual or sudden as a function of the network density? In the INTRODUCTION model, try varying the probability of introductions as opposed to random encounters. How does this affect the eveneness of the degree distribution and the number of closed triads formed? ## COPYRIGHT AND LICENSE This model was adapted by Lada Adamic from Uri Wilensky's Giant Component model in NetLogo's models library Copyright 2012 Lada Adamic. ![CC BY-NC-SA 3.0](http://i.creativecommons.org/l/by-nc-sa/3.0/88x31.png) This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/3.0/ or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA. @#$#@#$#@ default true 0 Polygon -7500403 true true 150 5 40 250 150 205 260 250 airplane true 0 Polygon -7500403 true true 150 0 135 15 120 60 120 105 15 165 15 195 120 180 135 240 105 270 120 285 150 270 180 285 210 270 165 240 180 180 285 195 285 165 180 105 180 60 165 15 arrow true 0 Polygon -7500403 true true 150 0 0 150 105 150 105 293 195 293 195 150 300 150 box false 0 Polygon -7500403 true true 150 285 285 225 285 75 150 135 Polygon -7500403 true true 150 135 15 75 150 15 285 75 Polygon -7500403 true true 15 75 15 225 150 285 150 135 Line -16777216 false 150 285 150 135 Line -16777216 false 150 135 15 75 Line -16777216 false 150 135 285 75 bug true 0 Circle -7500403 true true 96 182 108 Circle -7500403 true true 110 127 80 Circle -7500403 true true 110 75 80 Line -7500403 true 150 100 80 30 Line -7500403 true 150 100 220 30 butterfly true 0 Polygon -7500403 true true 150 165 209 199 225 225 225 255 195 270 165 255 150 240 Polygon -7500403 true true 150 165 89 198 75 225 75 255 105 270 135 255 150 240 Polygon -7500403 true true 139 148 100 105 55 90 25 90 10 105 10 135 25 180 40 195 85 194 139 163 Polygon -7500403 true true 162 150 200 105 245 90 275 90 290 105 290 135 275 180 260 195 215 195 162 165 Polygon -16777216 true false 150 255 135 225 120 150 135 120 150 105 165 120 180 150 165 225 Circle -16777216 true false 135 90 30 Line -16777216 false 150 105 195 60 Line -16777216 false 150 105 105 60 car false 0 Polygon -7500403 true true 300 180 279 164 261 144 240 135 226 132 213 106 203 84 185 63 159 50 135 50 75 60 0 150 0 165 0 225 300 225 300 180 Circle -16777216 true false 180 180 90 Circle -16777216 true false 30 180 90 Polygon -16777216 true false 162 80 132 78 134 135 209 135 194 105 189 96 180 89 Circle -7500403 true true 47 195 58 Circle -7500403 true true 195 195 58 circle false 0 Circle -7500403 true true 0 0 300 circle 2 false 0 Circle -7500403 true true 0 0 300 Circle -16777216 true false 30 30 240 cow false 0 Polygon -7500403 true true 200 193 197 249 179 249 177 196 166 187 140 189 93 191 78 179 72 211 49 209 48 181 37 149 25 120 25 89 45 72 103 84 179 75 198 76 252 64 272 81 293 103 285 121 255 121 242 118 224 167 Polygon -7500403 true true 73 210 86 251 62 249 48 208 Polygon -7500403 true true 25 114 16 195 9 204 23 213 25 200 39 123 cylinder false 0 Circle -7500403 true true 0 0 300 dot false 0 Circle -7500403 true true 90 90 120 face happy false 0 Circle -7500403 true true 8 8 285 Circle -16777216 true false 60 75 60 Circle -16777216 true false 180 75 60 Polygon -16777216 true false 150 255 90 239 62 213 47 191 67 179 90 203 109 218 150 225 192 218 210 203 227 181 251 194 236 217 212 240 face neutral false 0 Circle -7500403 true true 8 7 285 Circle -16777216 true false 60 75 60 Circle -16777216 true false 180 75 60 Rectangle -16777216 true false 60 195 240 225 face sad false 0 Circle -7500403 true true 8 8 285 Circle -16777216 true false 60 75 60 Circle -16777216 true false 180 75 60 Polygon -16777216 true false 150 168 90 184 62 210 47 232 67 244 90 220 109 205 150 198 192 205 210 220 227 242 251 229 236 206 212 183 fish false 0 Polygon -1 true false 44 131 21 87 15 86 0 120 15 150 0 180 13 214 20 212 45 166 Polygon -1 true false 135 195 119 235 95 218 76 210 46 204 60 165 Polygon -1 true false 75 45 83 77 71 103 86 114 166 78 135 60 Polygon -7500403 true true 30 136 151 77 226 81 280 119 292 146 292 160 287 170 270 195 195 210 151 212 30 166 Circle -16777216 true false 215 106 30 flag false 0 Rectangle -7500403 true true 60 15 75 300 Polygon -7500403 true true 90 150 270 90 90 30 Line -7500403 true 75 135 90 135 Line -7500403 true 75 45 90 45 flower false 0 Polygon -10899396 true false 135 120 165 165 180 210 180 240 150 300 165 300 195 240 195 195 165 135 Circle -7500403 true true 85 132 38 Circle -7500403 true true 130 147 38 Circle -7500403 true true 192 85 38 Circle -7500403 true true 85 40 38 Circle -7500403 true true 177 40 38 Circle -7500403 true true 177 132 38 Circle -7500403 true true 70 85 38 Circle -7500403 true true 130 25 38 Circle -7500403 true true 96 51 108 Circle -16777216 true false 113 68 74 Polygon -10899396 true false 189 233 219 188 249 173 279 188 234 218 Polygon -10899396 true false 180 255 150 210 105 210 75 240 135 240 house false 0 Rectangle -7500403 true true 45 120 255 285 Rectangle -16777216 true false 120 210 180 285 Polygon -7500403 true true 15 120 150 15 285 120 Line -16777216 false 30 120 270 120 leaf false 0 Polygon -7500403 true true 150 210 135 195 120 210 60 210 30 195 60 180 60 165 15 135 30 120 15 105 40 104 45 90 60 90 90 105 105 120 120 120 105 60 120 60 135 30 150 15 165 30 180 60 195 60 180 120 195 120 210 105 240 90 255 90 263 104 285 105 270 120 285 135 240 165 240 180 270 195 240 210 180 210 165 195 Polygon -7500403 true true 135 195 135 240 120 255 105 255 105 285 135 285 165 240 165 195 line true 0 Line -7500403 true 150 0 150 300 line half true 0 Line -7500403 true 150 0 150 150 link true 0 Line -7500403 true 150 0 150 300 link direction true 0 Line -7500403 true 150 150 30 225 Line -7500403 true 150 150 270 225 pentagon false 0 Polygon -7500403 true true 150 15 15 120 60 285 240 285 285 120 person false 0 Circle -7500403 true true 110 5 80 Polygon -7500403 true true 105 90 120 195 90 285 105 300 135 300 150 225 165 300 195 300 210 285 180 195 195 90 Rectangle -7500403 true true 127 79 172 94 Polygon -7500403 true true 195 90 240 150 225 180 165 105 Polygon -7500403 true true 105 90 60 150 75 180 135 105 plant false 0 Rectangle -7500403 true true 135 90 165 300 Polygon -7500403 true true 135 255 90 210 45 195 75 255 135 285 Polygon -7500403 true true 165 255 210 210 255 195 225 255 165 285 Polygon -7500403 true true 135 180 90 135 45 120 75 180 135 210 Polygon -7500403 true true 165 180 165 210 225 180 255 120 210 135 Polygon -7500403 true true 135 105 90 60 45 45 75 105 135 135 Polygon -7500403 true true 165 105 165 135 225 105 255 45 210 60 Polygon -7500403 true true 135 90 120 45 150 15 180 45 165 90 square false 0 Rectangle -7500403 true true 30 30 270 270 square 2 false 0 Rectangle -7500403 true true 30 30 270 270 Rectangle -16777216 true false 60 60 240 240 star false 0 Polygon -7500403 true true 151 1 185 108 298 108 207 175 242 282 151 216 59 282 94 175 3 108 116 108 target false 0 Circle -7500403 true true 0 0 300 Circle -16777216 true false 30 30 240 Circle -7500403 true true 60 60 180 Circle -16777216 true false 90 90 120 Circle -7500403 true true 120 120 60 tree false 0 Circle -7500403 true true 118 3 94 Rectangle -6459832 true false 120 195 180 300 Circle -7500403 true true 65 21 108 Circle -7500403 true true 116 41 127 Circle -7500403 true true 45 90 120 Circle -7500403 true true 104 74 152 triangle false 0 Polygon -7500403 true true 150 30 15 255 285 255 triangle 2 false 0 Polygon -7500403 true true 150 30 15 255 285 255 Polygon -16777216 true false 151 99 225 223 75 224 truck false 0 Rectangle -7500403 true true 4 45 195 187 Polygon -7500403 true true 296 193 296 150 259 134 244 104 208 104 207 194 Rectangle -1 true false 195 60 195 105 Polygon -16777216 true false 238 112 252 141 219 141 218 112 Circle -16777216 true false 234 174 42 Rectangle -7500403 true true 181 185 214 194 Circle -16777216 true false 144 174 42 Circle -16777216 true false 24 174 42 Circle -7500403 false true 24 174 42 Circle -7500403 false true 144 174 42 Circle -7500403 false true 234 174 42 turtle true 0 Polygon -10899396 true false 215 204 240 233 246 254 228 266 215 252 193 210 Polygon -10899396 true false 195 90 225 75 245 75 260 89 269 108 261 124 240 105 225 105 210 105 Polygon -10899396 true false 105 90 75 75 55 75 40 89 31 108 39 124 60 105 75 105 90 105 Polygon -10899396 true false 132 85 134 64 107 51 108 17 150 2 192 18 192 52 169 65 172 87 Polygon -10899396 true false 85 204 60 233 54 254 72 266 85 252 107 210 Polygon -7500403 true true 119 75 179 75 209 101 224 135 220 225 175 261 128 261 81 224 74 135 88 99 wheel false 0 Circle -7500403 true true 3 3 294 Circle -16777216 true false 30 30 240 Line -7500403 true 150 285 150 15 Line -7500403 true 15 150 285 150 Circle -7500403 true true 120 120 60 Line -7500403 true 216 40 79 269 Line -7500403 true 40 84 269 221 Line -7500403 true 40 216 269 79 Line -7500403 true 84 40 221 269 x false 0 Polygon -7500403 true true 270 75 225 30 30 225 75 270 Polygon -7500403 true true 30 75 75 30 270 225 225 270 @#$#@#$#@ NetLogo 5.0.1 @#$#@#$#@ set layout? false setup repeat 175 [ go ] repeat 35 [ layout ] @#$#@#$#@ @#$#@#$#@ @#$#@#$#@ @#$#@#$#@ default 0.0 -0.2 0 0.0 1.0 0.0 1 1.0 0.0 0.2 0 0.0 1.0 link direction true 0 Line -7500403 true 150 150 90 180 Line -7500403 true 150 150 210 180 @#$#@#$#@ 0 @#$#@#$#@