extensions [ nw ] breed [actors actor] breed [events event] breed [empty-events empty-event] breed [folded-actors folded-actor] breed [rands rand] undirected-link-breed [het-links het-link] ;; links between actors and events undirected-link-breed [hom-links hom-link] ;; folded links between actors undirected-link-breed [rand-links rand-link] ;; the links in the random network folded-actors-own [ cc nr-neighbors nr-hood-connections ] rands-own [ cc ] globals [ minimum maximum num_edges L L-rand C C-rand ] to setup clear-all cr_actors cr_events set minimum 2.3 set maximum 5.5 set num_edges (num_events / num_actors) + 1.5 ifelse num_edges < minimum [ set num_edges minimum ] [ if num_edges > maximum [ set num_edges maximum ] ] do_edges end ;;creates actor nodes to cr_actors set-default-shape actors "person" set-default-shape folded-actors "person" while [count actors < num_actors] [ create-actors 1 [ setxy -13 random-ycor ;(max-pycor - 2 - who) ] ] end ;;creates event-nodes to cr_events set-default-shape events "dot" set-default-shape empty-events "dot" create-empty-events num_events [ setxy 5 random-ycor ;(max-pycor - 2 - who + count actors) ] end to do_edges_priority ask empty-events [ set breed events ] let event-who one-of events ask actors [ create-het-link-with event-who [ set color 3 ;ask end2 [ set breed events ] ] create-het-link-with one-of events [ set color 3 set event-who end2 ] set label count link-neighbors ] ask events [ if count link-neighbors = 0 [ set breed empty-events ] ] end to do_edges_random ask actors [ ifelse count empty-events = 0 [ create-het-link-with one-of events [ set color 3 ] ] [ create-het-link-with one-of empty-events [ set color 3 ask end2 [ set breed events] ] ] ] ask empty-events [ if count link-neighbors = 0 [ create-het-link-with one-of actors [ set color 3 ] set breed events ] ] end to do_edges_rest ask actors [ while [ count link-neighbors < num_edges - 1 ] [ ifelse count empty-events = 0 [ create-het-link-with one-of events [ set color 3 ] ] [ create-het-link-with one-of empty-events [ set color 3 ask end2 [ set breed events] ] ] ] set label count link-neighbors ] end ;;create edges between actors and events to do_edges ;; to have completely randomly assigned edges, use this instead of do_edges_iterate ;do_edges_random ;; it's possible that the network is not connected then! do_edges_priority do_edges_rest while [count links < num_edges * num_actors] [ ask one-of actors [ ifelse count empty-events = 0 [ create-het-link-with one-of events [ set color 3 ] ] [ create-het-link-with one-of empty-events [ set color 3 ask end2 [ set breed events] ] ] ] ] ask actors [ set label "" ] ; for debugging purposes, to see if any events have remained disconnected ask events [ if count link-neighbors = 0 [ set breed empty-events ] ] ;show count empty-events end ;;folds the whole network to fold reset-ticks while [count events > 0] [ step ] end ;; this is one step to folding all the actors connected to one event together to step reset-ticks if count events > 0 [ ask one-of events [ if animation [ set color sky ask my-links [ set color cyan ] ask link-neighbors [ set color red ] ] let event-neighbors link-neighbors let ev-who who ask link-neighbors [ if animation [ if is-actor? turtle who [ setxy random -7 ycor ] set color cyan set shape "x" ] set breed folded-actors let act-who who ask event-neighbors [ if who != act-who [ create-hom-link-with turtle act-who if animation [ ask hom-link who act-who [ set color red ] ] set breed folded-actors ] ] repeat 30 [layout-spring folded-actors hom-links 0.2 4 1] set nr-neighbors count hom-link-neighbors set shape "person" if animation [ set color red ] ask hom-links [ set color 54 ] ask het-link act-who ev-who [ die ] ] ask event-neighbors [ set color lime ] die ] ] calc-cluster tick plotting end ;;calculates the Cluster-Coefficient and the Average Path Length to calc-cluster let C-temp 0 if (count folded-actors > 0) [ ask folded-actors [ let current self let nr-hood-links 0 ;set size ((count my-links / count hom-links) * 20) ask hom-link-neighbors [ set nr-hood-links (nr-hood-links + count hom-link-neighbors with [hom-link-neighbor? current] ) ;this counts every link twice ] set nr-hood-connections nr-hood-links if nr-hood-connections > 0 [ set cc nr-hood-connections / (nr-neighbors * (nr-neighbors - 1)) ] ;;what if no neighbors <= 1? if cc-show [ set label precision cc 2 ] set C-temp (C-temp + cc) ] set C (C-temp / (count folded-actors)) ; TODO division by zero error! nw:set-context folded-actors hom-links set L nw:mean-path-length carefully [ if not L [ set L 0 ] ][ print error-message ] ] end ;plot L and C for smallworldgraph to plotting set-current-plot "Clustering Coeff." set-current-plot-pen "CC" plotxy ticks C set-current-plot "Avg Pathlength" set-current-plot-pen "Avg L" plotxy ticks L ;set-current-plot-pen "CC" ;plotxy ticks C set-current-plot-pen "log(#a)" plotxy ticks log num_actors 2 end ;;do spring-layout for graph to do-layout ;ask folded-actors [ set size ((count my-links / count hom-links) * 20) ] ;ask folded-actors [ set size (cc * 2) ] repeat 50 [layout-spring turtles links 0.2 3 1] end ;;creates a random graph with the same number of nodes and the same number ;;of edges than the small world graph to create-random-graph if (count hom-links > 0) [ if (count rands = 0) [ set-default-shape rands "dot" create-rands num_actors [set color yellow] layout-circle rands max-pxcor - 15 ask rands [ left 10 ] ] tick ask rand-links [ die ] while [count rand-links < count hom-links] [ask one-of rands [ create-rand-link-with one-of other rands ]] nw:set-context rands rand-links set L-rand nw:mean-path-length ; should not happen too often, but if graph disconnected, nothing happens (no plotting!) if L-rand > -1 [ do-layout ;layout-tutte rands rand-links max-pxcor - 15 ;;check if connected! let C-temp 0 ask rands [ let current self let nr-hood-links 0 set cc 0 ask rand-link-neighbors [ set nr-hood-links (nr-hood-links + count rand-link-neighbors with [rand-link-neighbor? current] ) ;this counts every link twice ] if nr-hood-links > 0 [ set cc (nr-hood-links / (count rand-link-neighbors * (count rand-link-neighbors - 1))) set size (cc * 2) ] ;;what if no neighbors <= 1? if cc-show [ set label precision cc 2 ] set C-temp (C-temp + cc) ] set C-rand (C-temp / (count rands)) plotting set-current-plot "Avg Pathlength" set-current-plot-pen "Avg L rand" plotxy ticks L-rand ;;Do the random plots ;set-current-plot-pen "CC-rand" ;plotxy ticks C-rand set-current-plot "Clustering Coeff." set-current-plot-pen "CC-rand" plotxy ticks C-rand ] ] end @#$#@#$#@ GRAPHICS-WINDOW 280 10 792 578 -1 -1 13.63415 1 10 1 1 1 0 0 0 1 -18 18 -20 20 0 0 1 ticks 30.0 SLIDER 16 10 125 43 num_actors num_actors 50 100 50.0 1 1 NIL HORIZONTAL SLIDER 130 10 250 43 num_events num_events 50 200 50.0 1 1 NIL HORIZONTAL BUTTON 142 46 250 79 NIL Setup NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 106 90 249 123 Fold All Fold NIL 1 T OBSERVER NIL NIL NIL NIL 1 MONITOR 16 492 102 537 Pathlength L L 4 1 11 MONITOR 16 540 147 585 Clustering Coef C C 4 1 11 MONITOR 190 444 266 489 folded links count hom-links 17 1 11 BUTTON 17 90 102 123 One Step step NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 116 129 249 162 Random Graph create-random-graph T 1 T OBSERVER NIL NIL NIL NIL 1 MONITOR 150 540 237 585 CC-random C-rand 4 1 11 MONITOR 106 492 187 537 log(#actors) log num_actors 2 4 1 11 MONITOR 15 444 115 489 #edges / actor num_edges 4 1 11 SWITCH 17 46 138 79 animation animation 1 1 -1000 MONITOR 189 492 278 537 log(log(#a)) log log num_actors 2 2 4 1 11 PLOT 21 181 250 301 Avg Pathlength ticks Avg L 0.0 100.0 0.0 8.0 true true "" "" PENS "log(#a)" 1.0 0 -1184463 true "" "" "Avg L rand" 1.0 0 -955883 true "" "" "Avg L" 1.0 0 -5825686 true "" "" "CC" 1.0 0 -14835848 false "" "" "CC-rand" 1.0 0 -10899396 false "" "" PLOT 21 301 250 421 Clustering Coeff. # random graphs CC 0.0 10.0 0.0 1.0 true true "" "" PENS "CC" 1.0 0 -14835848 true "" "" "CC-rand" 1.0 0 -10899396 true "" "" TEXTBOX 20 132 107 162 Execute after\nFold All: 12 0.0 1 SWITCH 16 588 128 621 cc-show cc-show 1 1 -1000 MONITOR 118 444 187 489 het-links count het-links 17 1 11 @#$#@#$#@ ## WHAT IS IT? This model explains the small world phenomenon via the use of actors and events. Actors vistit certain events and are connected through other actors through the events. In the step/fold process, we develop a network of only actors (where before there was an affiliation network of actors and events) to see whether it is a small world network. ## HOW IT WORKS The model has different kinds of agents or nodes: actors, events and random nodes. First we build the two-mode network of actors and nodes, fold it so that we have a one node network of only actors and compare it to a random network. ## HOW TO USE IT The user can control the number of actor-/event-nodes through the first two sliders. The minimum number of nodes is 50, with 100 actors maximum and 200 events maximum. The number of nodes per actors are calculated automatically and can be seen at the monitor "# edges / actor". By pressing Setup the affiliation network is painted to the screen, with the icons on the left side (people) as actors and on the right hand side events (dots). As the next step in the algorithm, we need to fold this network so that we have a one-mode network consisting only of actors who are connected by the events they visited. Two buttons provide this functionality: "one step" shows the folding process in detail by examining the folding of one event. The corresponding actors are linked to each other and the event is deleted. The folded actors are visualized by using green colour for the vertices as well as the edges between them. If you wish to see the process in more detail, slow down the speed and turn on animation. By pressing "Fold All" all the remaining events will be processed, completing the folding process. The result is a connected (should be in most cases, although there is no guarantee) graph consisting only of actors (green people and lines). This graph has a certain average path length which can be seen in it's monitor and on the Plot. The average path length is very short for small world networks, and can be described as proportional to the log(number of nodes) or for scale free networks the log(log(number of nodes)). For the second factor we have already calculated the clustering coefficient for each node (you can turn the display for each node on/off) and it's average and plotted it. Now we need to compare the data of our graph with a random graph, so you need to press "random graph", which creates a new random graph with the same amount of nodes and number of edges as our folded network with each step. Because a single random graph is not representative, the model creates new graphs on a loop until you stop it by pressing "random graph" again. The CC-value is drawn in both plots. ## THINGS TO NOTICE Use both monitors and plots to determine whether or why the folded network is a small-world network. Is the clustering coefficient higher than the clustering coefficient of the random network? What is the size of the average path length? Is it better to have a smaller or a higher path length? ## THINGS TO TRY See what habens when you have significantly more actors than events or vice versa. also see what happens when the number of actors and events are virtually the same. If you're curious what the clustering coefficient of single nodes is you can enable the cc-show switch. If you'd like to see the folding process in more detail, turn on the animation switch and slow down the speed of the model. ## EXTENDING THE MODEL This section could give some ideas of things to add or change in the procedures tab to make the model more complicated, detailed, accurate, etc. The way the edges are drawn in the affiliation network is only seemingly random. We decided on a minimum and maximum amount of edges per actors (2.3/5.5), so every actor has minimum 2 or 3, max 5 or 6 connections. to ensure that the network is connected, we first draw a path with the connections, connecting actor a to event b, and event b to event c and so on. the rest of the edges are then drawn randomly. To change this, you can use the do_edges_random instead of do_edges_with_priority subprocedure in the do_edges procedure. This may however result in a not connected graph, which cannot demonstrate small world properties. ## NETLOGO FEATURES This section could point out any especially interesting or unusual features of NetLogo that the model makes use of, particularly in the Procedures tab. It might also point out places where workarounds were needed because of missing features. ## RELATED MODELS This section could give the names of models in the NetLogo Models Library or elsewhere which are of related interest. ## CREDITS AND REFERENCES This section could contain a reference to the model's URL on the web if it has one, as well as any other necessary credits or references. @#$#@#$#@ 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 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