network science with netlogo tutorial · network science with netlogo version 05/07/2017 7 • make...

NetworkSciencewithNetlogo version05/07/2017

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NetworkSciencewithNetlogoTutorialByTomBrughmans

Firstversion:March2016

Thisversioncreated05/07/2017

Netlogoversionused:6.0.1

Extensionused:nw(pre-packagedwithNetlogo6.0.1)https://github.com/NetLogo/NW-Extension

Citethistutorialas:

Brughmans,T.(2016).NetworkSciencewithNetlogoTutorial,https://archaeologicalnetworks.wordpress.com/resources/#netlogo.

1. IntroductionThistutorialprovidesanintroductiontocreatingagent-basednetworkmodelswithNetlogo.Byworkingthroughthistutorialyouwilllearnhowtocreatenodes,createedges,performlayoutsintroduceprobabilityinedgecreation,createatradeprocessworkingonthenetworkandhowtoderivenetworkmeasures.

2. Conventions,tipsandassumedknowledgeThistutorialassumesbasicknowledgeofNetlogoandofsimulation.ItisrecommendedtowalkthroughtheintroductorytutorialsontheNetlogowebsiteorthetutorialonNetlogoforarchaeologistsontheSimulatingComplexityblog:

https://simulatingcomplexity.files.wordpress.com/2014/07/dispersal_tutorial.pdf

https://ccl.northwestern.edu/netlogo/docs/

Thistutorialwillalsorefertosomenetworksciencejargon,conceptsandtechniques.Youcangetabasicdefinitionofallofthesefromtheglossaryonmyblog:

https://archaeologicalnetworks.wordpress.com/resources/#glossary

Goodintroductionstonetworkscienceincludethefollowing:

Brandes,U.,Robins,G.,McCranie,A.,&Wasserman,S.2013.Whatisnetworkscience?NetworkScience1(01):p.1–15.

Newman,M.E.J.,2010.Networks:anintroduction,Oxford:OxfordUniversityPress.

Codewritteninthistutorialwillbeformattedasinthefollowingexample:breed [nodes node]

Saveyourproject!Dothisregularlyandusemultipleversionsthroughoutthetutorialsothatyoucanfallbackonanearlierversionatanytime.Iwillremindyouregularlythroughoutthetutorialtosaveyourproject.


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3. DownloadandinstallNetlogoNetlogoisopensourcesoftwareandcanbedownloadedfreeofchargeforWindows,MacOSXandLinux.

Gotohttps://ccl.northwestern.edu/netlogo/download.shtml.

DownloadtheNetlogoinstaller(thistutorialusesversion6.0.1).

RuntheinstallerandinstallNetlogo.

4. Netlogoresources,manualandinterfaceNetlogohasgreatdocumentationaboutallitsfeaturesandcodeinitsusermanual:https://ccl.northwestern.edu/netlogo/docs/

Thismanualincludestutorials,areferencetothesoftwarefunctions,adictionarytoitsprogramminglanguage,documentationofitsextensionsandmuchmore.

Additionalexternalresourcescanbefoundontheresourcespage:

https://ccl.northwestern.edu/netlogo/resources.shtml

AdetailedreferencetoNetlogo’sInterfacecanbefoundhere:https://ccl.northwestern.edu/netlogo/docs/

ThistutorialwillonlygiveaverybriefintroductiontothekeyelementsoftheNetlogointerfaceyouwillbeusingthroughoutthetutorial.


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WhenyouopenNetlogoitshouldlooksomethinglikethis:

Ithasthreetabs:Interface,Info,Code.

TheInterfacetabiswhereyouwatchyourmodelrun.Throughoutthetutorialyouwilladdbuttonsandsliderstocontrolthevariablesofyourmodel,andyouwilladdmonitorsandplotstoinspectwhatyourmodelisdoing.Youcanspeeduporslowdownthesimulationusingthespeedslideratthetopoftheinterface.Thecommandcenteratthebottomwilldisplaymessagesyouaskthemodeltoproduce,andyoucanalsouseittogivetocommandstothemodelfromtheinterfacetab.


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TheInfotabiswhereyoudescribeyourmodelusingastandardizedsetofquestions.Addingthisinformationwhenyoushareyourmodelwithotheriscrucialtoenablethemtoworkwithyourmodel.WewillnotworkwiththeInfotabinthistutorial.

TheCodetabiswhereyouwriteandstorethecodeforthemodel.InthistutorialwewillbemainlyworkingintheCodetab.AusefulfeatureistheCheckfunctionatthetopofthistab:clickthistoletNetlogocheckyourcodeforerrors.Ifitfindserrorsthenyouwillbeguided


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totheerrorandaskedtoresolveitbeforeyoucancontinue,ifitdoesnotfinderrorsthenyoucanproceedwithcodingorviewingyourmodelinaction.NOTE:thiserrorcheckeronlycheckswhethertheprimitivesusedandtheorderofthecodecomplywiththeNetlogorules(i.e.thecode’svocabularyandgrammar).Itwillnotcheckwhetherthecodedoeswhatyouwantittodo,sogettingnoerrorsisnoguaranteethatthecodeworksthewayitshouldorthewayyouthinkitdoes.Theerrorcheckerwillalwaysneedtobeusedalongsideothererrorcheckingtechniques,likereportingvariablevaluesandcheckingthemagainstexpectations,ortestingsubmodelsindependently.

5. NetlogodictionaryAcrucialresourcewhencodinginNetlogoisitsdictionary:https://ccl.northwestern.edu/netlogo/docs/

Forthistutorial,youwillfindthesectionon‘Links’intheNetlogodictionaryparticularlyuseful,aswellasthedocumentationofthe‘nw’extension.

Youcangetdirectaccess(evenoffline)totheentryaboutaparticularprimitivebyright-clickingitandselectingQuickHelp.


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6. CreatenodesNetworksconsistofatleasttwothings:asetofnodesandasetofedges(networksciencejargonforanundirectedrelationship).NodesandedgesinNetlogoareatypeofagents,orturtlesinNetlogojargon.WewillfirstcreatethenodesinNetlogo.

Toavoidusingtheconfusingterm‘turtles’torefertoournodes,wewillcreateanewbreedofagentscalled‘nodes’.Abreedisasetofagentsthatisgivenaspecificnameandcanbecommandedusingspecificvariablesgiventothisagentset.

Tocreateabreed,writeatthetopoftheCodetab:breed [nodes node]

Ifyouclickthecheckboxnowyouwillnoticethattherearenoerrors,sowecancontinuetocode.

Saveyourmodel!

TocreateanumberofnodesandvisualisethemintheInterfacewewillcreateasetupprocedure.AddthefollowingbelowthebreedcommandintheCodetab:

to setup clear-all reset-ticks end

ThisisastandardsetupprocedureinNetlogothatresetstheNetlogointerfaceofanysettingsfromprevioussimulationsandresetstheticksto0toinitiateanewsimulation(Netlogojargonforatimestep).Settingupasimulationmeanswearereadytorunthesimulation.

Nowwewilladdcommandstothisstandardsetupproceduretocreateournodes.Expandtheproceduretothefollowing:

to setup clear-all set-default-shape nodes "circle" create-nodes 50 reset-ticks end

Oursetupprocedurewillnowcreate50nodes,andtheywillberepresentedascircles.Toseethisinaction,wewillneedtoaddabuttonintheInterfacetab.DothefollowingintheInterfacetab:


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• Makesurethedropdownboxnexttothegreenplussignhas‘Button’selected.• Clickthegreenplussigncalled‘Add’(seefigurebelow).Yourcursorwillbecomea

bigplussign.• Clickanywhereinthewhitespacenexttotheblackinterfacewindow.Abuttonwill

appearandanewwindowwillopenwhereyoucandeterminewhatthisbuttonwillbeusedfor.

• WritesetupinthecommandsboxofthisnewwindowandclickOK(seefigurebelow).


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Youjustcreatedabuttoncalled‘setup’.WhenyoupressthisbuttonthesetupprocedurewewroteintheCodetabwillbeexecuted.Tryit!

Youwillseeacirclebeingcreatedattheverycentreoftheinterfacewindow.Althoughitlookslikeasinglenode,wehaveactuallycreated50nodesthatareallplacedontopofeachotherinthecentreofthewindow,becausewedidnotspecifywheretheyshouldbeplaced.Right-clickthenodeandyouwillnoticethereare50overlappingnodesasinthisfigure:

Wewillsolvethisissueofnodeplacementsoon,butfirstweshouldgiveourselvesmorecontroloverthenumberofnodes.Nowwehave‘hard-coded’thenumberofnodesinourCodetab,whichmakesitalotofworktochangethenumberofnodeswhenexploringourfinalmodelandrunningsimulationexperiments.

Toovercomethisissuewewillnowaddavariablethatcontrolsthenumberofnodes.IntheCodetab,replacecreate-nodes 50with:

create-nodes num-nodes

Wehavenowcreateavariablecallednum-nodeswhichwilldeterminehowmanynodesarecreatedbycreate-nodes.Whenyouclicktheerrorchecker,youwillnoticethatNetlogohasfoundanerror:“NothingnamedNUM-NODEShasbeendefined.Thisisbecausewehavewrittenavariablethathasnotbeendefinedearlierinthecodeorontheinterface.Wewanttocontrolthevariableintheinterfacewithaslidersothatwecaneasilychangeitwhenrunningoursimulation.

ToovercomethiserrorandcontrolthisvariableintheInterfacetabdothefollowing:

• Clickthedropdownmenunexttothe‘Add’button.• Select‘Slider’.Yourcursorwillchangeintoalargeplussign.• Clickinthewhitespacebelowthe‘setup’button.Asliderwillbecreatedandanew

windowwillopenwhereyoucandeterminewhatthissliderwillbeusedfor.


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• Wewillusethisslidertocontrolthevariablenum-nodes,sowritenum-nodesinthebox‘globalvariable’.Setthe‘minimum’to2andclickOK(seefigurebelow).

Youhavenowcreatedasliderwhereyoucanmodifyhowmanynodesyoucreate.Youwillalsonoticethattheerrormessageonthecodetabnolongerappears.

Butthenodesarestilloverlapping,solet’stakecareofthatrightnow!

Saveyourmodel!

7. CircularlayoutYoucanplaceyournodesinmanydifferentwaysdependingonwhatfeatureofthenetworkyouwishtoemphasise,aswewillseelaterinthetutorial.Butsinceweonlyhavenodesandnoedgesyet,let’sjustplaceallnodesalongacircularlayouttoavoidoverlappingnodes.

IntheCodetabaddthefollowingafterthelinecreatingthenodes:layout-circle nodes 10

WehaveusedaNetlogocommandthatpositionsnodesalongacirclewitharadiusof10inarandomorder.IfyougototheInterfacetabnowandclickthesetupbuttonthenyournodeswillbepositionedalongacircleasinthisfigure:


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However,youmightwantmorecontrolovertheorderinwhichthenodesareplaced,andnotjustletthembeplacedinarandomorder.Toachievethis,reworkthelayoutlineintheCodetabtoreadlikethis:

layout-circle sort nodes 10

IfyouclickthesetupbuttonintheInterfacetabnow,youwillgetacircularpositioningofallnodes,buttheyareorderedaccordingtotheir‘Who’number(theuniqueIDofaturtleassignedbyNetlogowhenitiscreated)clockwisestartingfromthetopmiddlenodeinthecircle.Youcancheckthisbyrightclickingthenodesinorderandyouwillnoticethattheorderofnodesis0,1,2,3,….(seefigurebelow).


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However,onceagainwehard-codedsomethingthatisnotveryflexibleifthemodelenvironmentchanges:thecircleradiusof10.Itwouldbefarbetterifthisradiuswasdefinedbytheresolutionoftheinterfacewindow(i.e.themodel’s‘World’settingsexpressedincoordinates,whichcanbeviewedbyright-clickingtheinterfacewindowandselecting‘Edit’).

IntheCodetabchangethelayoutlinetothefollowing:layout-circle sort nodes max-pxcor - 1

WhenyouclickthesetupbuttonnowontheInterfacetabthecircularlayoutwillhavearadiusequaltotheradiusoftheinterfacewindow(i.e.theWorld’smax-pxcor)minus1topreventitfrombeingtooclosetotheedgesofthewindow:


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Saveyourmodel!

8. Networkcreationprocedures:whydoyoucreateanetworkmodel?

Nowthatwehaveasetofnodeswecancreateasetofedgesconnectingthenodes.

Thewayinwhichnodesareconnectedintoanetworkwilldependonyourresearchcontext,andultimatelywillberootedinyourreasonsfordecidingtobuildanetworkmodelinthefirstplace.Edgescouldberandomlyconnected,edgescanbeinformedbyempiricalobservations,orthenetworkstructurecouldrepresentahypothesisedsocial/spatial/othernetworkstructure.

Inthistutorialwewillrandomlycreateanetworkstructure,usingtheErdős–Rényirandomgraphmodel(fromnowonreferredtoasERmodel):anetworkconstructedbyconnectingrandomlyselectedpairsofnodeswithacertainprobabilityindependentfromeveryotheredge.https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93R%C3%A9nyi_model

Thisisthemostcommonwayofrandomlycreatingnetworks.Suchnetworksareveryusefulforcomparisonwithhypothesisedsocialprocesses,i.e.processescreatingedgeswithprobabilitiesdependentonotheredges.Forexample,acommonhypothesisforsocialnetworksoffriendshipistheideathatapairofunrelatedindividualshasahigherprobabilityofbecomingfriends(i.e.ofcreatinganedgebetweenapairofnodes)iftheyhaveafriendincommon(i.e.theprobabilityofthenewedgeisdependentontheexistenceofotheredges).NodesAandBinthefigurebelowhavenodeCasamutualfriend,soaccordingtothishypothesistheedgebetweenAandBwillbemorelikelytoappear:


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Wecancreatesimulationmodelsrepresentingthishypothesisednetworkcreationprocessandtherandomprocess,andcomparehowtheresultingnetworksdiffer.Canobservedfriendshiprelationshipsbereproducedthrougharandomprocess?Cantheybebetterreproducedthroughanotherhypothesisedprocess?Whatarethestructuralfeaturesofthenetworksarisingfromthehypothesis?

Decidinghowtoconnectnodesthroughedgesinyournetworkwilldependentirelyonyourresearchaimsandcontext.Tothinkaboutwhatmightbethemostappropriatewayofcreatingedgesinyourcontextyoucouldaskyourselfthefollowingquestions:

• WhydidIdecidetomakeanetworkmodel?• Whatarethenodesinmynetwork?• Whataretheedgesinmynetwork?• Arenodesandedgestakenfromempiricalobservations?• Willthenetworkmodelrepresentahypotheticalscenariothatwillbecompared

withempiricalobservations?• Whyarerelationshipsimportantinmyresearchcontext?• Howarerelationshipsdependentoneachother?• Whatkindsofconfigurationsorpatternsofedgesareimportant?• Whataremyhypothesesabouthowedgesarecreated?

9. CreateedgesRelationshipsinNetlogoarecalled‘links’andtheycanbeusedinasimilarwayas‘turtles’.Theycanbeeitherundirectedinwhichcasenetworkscientistsrefertothemas‘edges’,ortheycanbedirectedwhicharecommonlycalled‘arcs’.

Wewillcreateanewbreedofundirected‘links’called‘edges’.IntheCodetabbelowthepreviousbreedaddthefollowing:

undirected-link-breed [edges edge]

NowthatwehavecreatedabreedwecanstartimplementingtheproceduretocreateanERrandomgraphmodel.Wewilldothisinseveralsteps,slowlybuildingupthelinesofcode.

Inthesetupprocedure,addanewproceduretoconnectnodesafterthelayoutofthenodes:

connect-nodes


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Yourmodelshouldnowlooklikethis:breed [nodes node] undirected-link-breed [edges edge] to setup clear-all set-default-shape nodes "circle" create-nodes num-nodes layout-circle sort nodes max-pxcor - 1 connect-nodes reset-ticks end

Whenyouclicktheerrorcheckeritwillgiveyouanerrorsaying‘connect-nodes’hasnotbeendefined.Wewillnowaddanewprocedurecalledconnect-nodesbelowthesetupprocedure:

to connect-nodes end

Thiswillresolvetheerrormessage.

Asafirststepwewilladdthefollowingcommandinthisnewprocedure:to connect-nodes repeat 100 [ ask one-of nodes [create-edge-with one-of other nodes] ] end

Thiscodewillselect100nodesrandomlyinturnandeachnodewillbeaskedtocreateanedgewithanotherrandomlyselectednode.

NotethatthenormalcommandforcreatinglinksinNetlogoiscreate-link-with.Butbecausewehavecreatedabreedcallededges,wecanmodifythistocreate-edge-with.HavealookattheNetlogodictionaryformoreinformation:https://ccl.northwestern.edu/netlogo/docs/.

However,nowwhenyouclickthesetupbuttonontheInterfacetabyouwillgetaweirdnetworkwhereedgesseemtocrossthebordersoftheinterfacewindow:


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ThishappensbecausebydefaulttheNetlogo‘World’willwraparoundthehorizontalandverticaledges.Thisdoesnotmakemuchsensewhenmakinganetworkmodel!Attheveryleastitisnothelpfulforvisualexploration.Toavoidtheedgesfromcrossingtheseboundaries,right-clicktheinterfacewindow,selectEdit,andintheModelsettingswindowunchecktheboxesfor‘Worldwrapshorizontally’and‘Worldwrapsvertically’:

Whenyoudothis,thenetworkwilllooksomethinglikethis(notethatyournetworkwilllookdifferentbecausetheedgesarerandomlycreated):


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WenowneedtoaddanumberoffeaturestomakethisarealERmodel.Thecurrentcodestillallowsforpairsofnodestobeconnectedthatarealreadyconnected,andthenumberofedges(currently100)shouldnotbehard-codedbutratherreflectadesiredfeaturelikethedesireddensityofthenetwork.Networkdensityisdefinedasthefractionofthenumberofedgesthatarepresenttothemaximumpossiblenumberofedgesinthenetwork.

First,wewillasknodestoonlyconsidercreatinganedgewithanodethatitisnotyetconnectedto,bymodifyingtheedgecreationlinetothis:

ask one-of nodes [create-edge-with one-of other nodes with [edge-with myself = nobody]]

Inthiscode,‘myself’referstothenodethatdoestheasking,i.e.thenodeweselectinthefirstlineofthiscode.

Second,wewillreplacethe100toonlycreatethenumberofedgesneededtocreatethedesireddensity.IntheCodetabreplacerepeat 100 withthefollowing:

repeat (target-density * (((num-nodes * num-nodes) - num-nodes)) / 2)

Thisisacalculationofdensityinundirectednetworks.Themaximumnumberofedgesinsuchanetworkcanbecalculatedas:themaximumnumberofedgesisthenumberofnodestimesthenumberofnodes,minusthenumberofnodes(i.e.nodescannotbeconnectedtothemselves),anddividedbytwo(i.e.edgesarenotdirected:indirectednetworkstherearedoubleasmanymaximumlinksbecausetheycangointwodirections).Sincethedensitymeasurerepresentsacertainfractionofthismaximumnumberofedges,wemultiplyitbythevariabletarget-density,whichrepresentthedensitywedesireforournetwork:0representsnoedges,0.5representshalfthemaximumnumberofedgesbeingpresent,1representsallthemaximumnumberofedgesbeingpresent.

Whenyouclicktheerrorcheckeryouwillnoticeanerrorbecausewehavenotyetdefinedthevariabletarget-density.WewilladdthisvariableintheInterfacetabasaslider:

• Makesure‘Slider’isselectedinthedropdownbox.


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• Clickthe‘Add’button.• Clickinthewhitespacebelowthe‘num-nodes’slider.Awindowwillappear.• Entertarget-densityinthe‘Globalvariable’field.Theminimumwillbe0,the

increment0.05,themaximum1andtheValue(defaultvalue)0.5.ClickOK.

Theerrormessagewillberesolved.

Nowwhenyouclickthesetupbuttonyournetworkwillalwayshaveonlysomanyedgesasrequiredtoreachthedesireddensity.Forexample,ifyournetworkhas40nodesandyourdesireddensityis0.5thenyouwillcreate390edges:

0.5 ∗40 ∗ 40 − 40

2 = 390

Note:ifyougeta‘RuntimeError’atthispoint,click‘Dismiss’.Wewillresolvethiserrorlater.

However,youdon’tknowhowmanyedgesthereareuntilyoucountthem!Neitherdoweknowwhetherthenetworkactuallyhasthecorrectdensityuntilwecalculateit.Thereareafewwayswecoulddothis:usingtheCommandCenterorusingmonitors.

IntheCommandCentercommandlineatthebottomoftheInterfacetabwritethefollowing:

Show count edges

TheresultwillappearintheCommandCenterwindow:


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Amoreconvenientwaytocounttheedgesistoaddamonitorthatwillshowyouthenumberofedges.IntheInterfacetabdothefollowing:

• SelectMonitorfromthedropdownbox.• Clickthe‘Add’button.• Clickanywhereinthewhitespace.Anewwindowwillappearwhereyoucan

determinewhatwillbereported.• Writecount edgesinthe‘Reporter’box,setdecimalplacesto1(thereshouldbeno

decimalsbutitisgoodtoaddthisforerrorchecking:ifyouseeadecimalnumberinareporterwindowwhereyoudon’texpectit,youknowyoudidsomethingwrong).

Whenyouclickthesetupbuttonyouwillautomaticallyseethenumberofedgesinthemonitorboxyoujustcreated.

Nowwewillcreateamonitorforthedensity.IntheInterfacetabdothefollowing:


determinewhatwillbereported.• Writecount edges / (((num-nodes * num-nodes) - num-nodes) / 2)inthe

‘Reporter’box,setdecimalplacesto2,andsettheDisplayNameto‘density’(otherwisethedisplaynameofthismonitorwillbetheentirecommandweenteredintheReporterbox).Thiscommandcalculatesthefractionofthenumberofedgesthatarepresentoverthemaximumnumberofedges.Thenumberthatthismonitorgivesyoushouldthereforebethesameasthesettingofthetarget-densityvariable.Ifitisnot,thenyouknowyoudidsomethingwrongsoyoucansearchfortheproblemandfixit.


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However,thereisaproblemwiththiscode.Whenyouputthetarget-densityvariablehighthenyouwilloftengeta‘RuntimeError’.ThisErrorisveryinformativeandwillhelpusresolveit.Ithighlightsthepartofthecodewheretheproblemliesandtellsusitcannotfindanotherturtle(i.e.node)thatfitsthecriteria:

Theerrortellsusthatweareaskinganodetoidentifyanothernodeitisnotyetconnectedto,whensuchanodedoesnotexist:i.e.theaskingnodeisalreadyconnectedtoallothernodes.


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Weresolvethiserrorbyspecifyingthatwewillonlyasknodesthatarenotyetconnectedtoallothernodes,byaddingthefollowingcode:

ask one-of nodes with [count edge-neighbors < (num-nodes - 1)]

Theconnect-nodesprocedurewillnowlooklikethis:to connect-nodes repeat (target-density * (((num-nodes * num-nodes) - num-nodes)) / 2) [ ask one-of nodes with [count edge-neighbors < (num-nodes - 1)] [create-edge-with one-of other nodes with [edge-with myself = nobody]] ] end

Note:inNetlogowecallapairofnodesthatareconnectedlink-neighbors,butsincewecreatedabreedcallededgeswecallcanusethecommandedge-neighbors.

Saveyourmodel!

10. ProbabilityofedgecreationInordertogetanERmodelweneedtochangeonefinalthing:edgesneedtobecreatedwithacertainprobability.Inourcurrentcodeapairofnodesisrandomlyselectedandconnected,whereasinanERmodelthispairisonlyconnectedwithacertainprobability.Beingabletoattachprobabilitiestothecreationofedgesisveryimportantandusefulwhenyouwanttoexpressyourownhypothesesofnetworkcreation.Forexample,inthefriendshipnetworkhypothesismentionedabovewestatedthattheprobabilityofsomeedgesbeingcreatedishigherthanthatofothers:peoplewithmutualfriendswillbemorelikelytobecomefriendsthemselves.

Herewewillintroduceasimplemethodofcreatingedgeswithaprobabilityvariablethatyoucanmanipulatetorepresentyourhypothesisofnetworkcreation.

First,wemodifytheconnect-nodesproceduretoonlycreateanedgeifarandomfloatingpointnumberbetween0and1issmallerthanthenewvariableedge-probability:

ask one-of nodes with [count edge-neighbors < (num-nodes - 1)] [if random-float 1 < edge-probability [create-edge-with one-of other nodes with [edge-with myself = nobody]] ]

Wenowgetanerrormessagebecausethenewvariabledoesnotexistyet,sodothefollowingintheInterfacetab:

• SelectSliderfromthedropdownbox.• Clickthe‘Add’button.• Clickanywhereinthewhitespace.Anewwindowwillappearwhereyoucan

determinewhatthesliderwilldo.• Writeedge-probabilityinthe‘Globalvariable’box,settheminimumto0,the

incrementto0.05,themaximumto1andthedefaultvalueto0.5.ClickOK.


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Ifthisvariableissetto1thenanedgewillalwaysbecreated,ifitissetto0itwillneverbecreated,ifitissetto0.5itwillbecreated50%oftimes.

Whenyouclickthesetupbuttonnowyouwillnoticesomethingiswrongthankstoyourmonitors:thedensityinthemonitorisnotthesameasthetarget-densitysliderandthecount edgesmonitorreportsadifferentvalueeverytimeyoupressthesetupbutton.Thisisbecausethisprocessisrepeatedafixednumberoftimes,butnoteverytimeanedgeiscreated.

Asecondchangeisneeded,thistimereplacingthecoderepeatingthecreationofedges.Wewillimplementthisbycalculatinghowmanyedgesweneedtohaveattheendoftheprocedure(storedasthevariabletarget-edges),andcountinghowoftenanedgeisactuallycreated(weletavariablecalledcounterstartat0,onlywhenanedgeiscreateddoweaddonetothecounter:set counter counter + 1).Weonlystoptheprocedureifwehavecreatedthedesirednumberofedges(weusethewhile [counter < target-edges]commandtorepeattheprocessuntilthevariablecounterequalsthevariabletarget-edges).

Modifytheconnect-nodesproceduretoreadlikethis:to connect-nodes let target-edges (target-density * (((num-nodes * num-nodes) - num-nodes)) / 2)

let counter 0 while [counter < target-edges] [ ask one-of nodes with [count edge-neighbors < (num-nodes - 1)] [if random-float 1 < edge-probability [ create-edge-with one-of other nodes with [edge-with myself = nobody] set counter counter + 1 ] ] ] End

Whenyoupressthesetupbuttonyouwillnoticethatthemonitorsreportwhattheyshould.


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Saveyourmodel!

11. Force-directedlayoutNowthatwehaveasetofnodesandasetofedges,wecanplaceournodesinamoreinterestingwaythanjustacircle:wecanuselayoutalgorithmstohighlightstructuralfeaturesofthenetworktoaidvisualexplorationofthenetwork.Wewilldothisbyusingapopularforce-directedlayoutalgorithmcalledtheFruchterman-Reingoldlayoutalgorithm.Itissometimescalledaspring-embeddedlayoutbecausetheedgesactlikespringsbetweenthenodesthatrepeleachother.Moreonforce-directedlayoutalgorithmscanbefoundhere:https://en.wikipedia.org/wiki/Force-directed_graph_drawing

Netlogomakesitincrediblyeasytoimplementthis.Wewillcreateanewprocedurecalledlayout,usingtheNetlogocommand layout-spring.Addthefollowingcodebelowtheconnect-nodesprocedure:

to layout layout-spring nodes edges 0.2 5 1 end

Right-clickthelayout-springcommandtoaccesstheNetlogodictionaryandfindoutwhatthiscodedoes.Itwillperformthelayoutconsideringtheagent-setnodesasthenodesandthelink-setedgesastheedges.Thethreenumbersarevariablesofthealgorithmdeterminingfeaturesofthe“springs”:theirresistance,lengthandrepulsion.

InordertousethisnewlayoutprocedureweneedtoaddabuttontotheInterfacetab:

• SelectButtonfromthedropdownbox.• Clickthe‘Add’button.• Clickanywhereinthewhitespace.Anewwindowwillappearwhereyoucan

determinewhatthebuttonwilldo.• Writelayoutinthe‘Commands’box.ClickOK.

Nowyoucanpressthelayoutbuttontoperformthelayout.


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Notethatthisalgorithmworksdifferentlyfromthecircularlayout.Itdoesnothaveonesingle‘best’outcome,butinsteadwilliterativelychangethepositionofonenodeafteranothertakingintoaccountthe“springs”thatconnectnodes.Themoreyouclickthelayoutbutton,themorethenodeswillfindasuitableposition.

Thisalgorithmismostusefulforvisualexplorationwithlowdensitynetworks.Trytosetyourtarget-densitysliderlowandperformthelayout:thealgorithmwillrevealinterestingstructuralfeaturesthatarehiddeninthecircularlayout,suchasisolatednodes,nodeswithonlyoneconnection,andsetsofnodesthatarealltightlyconnectedwitheachother.

Randomlycreatednetworksaretypicallyverydenseandrarelyshowstrikingstructuralfeaturesinforce-directedlayouts.However,thisgroupoflayoutalgorithmisgreatatrevealingstructuralfeaturesthatarecommoninsocialnetworks:denseclustersand“bridging”nodesconnectingdifferentclusters.

Trychangingthevaluesofthethreenumbersinthelayout-springcommand.Youwillnoticethattheeffectofthespringsworksdifferently.Bychangingthesevariablesyouwillbeabletotailoryourlayoutalgorithmtomostappropriatelyhighlightthosestructuralfeaturesofyournetworkyouwanttoexploreorvisualise.Trychangingthevaluesinsuchawaythatitprovidesamoreinterestingrepresentationofaverydenserandomnetwork.

Saveyourmodel!

12. NetworkmeasuresWealreadyintroducedthreeimportantmeasuresofyournetworkstructure:thenumberofnodes,thenumberofedgesandthenetworkdensity.Nowwewillcalculateandreporttwomoremeasures:averagedegreeandaverageshortestpathlength.

Thedegreeofanodeisdefinedasthenumberofedgesconnectedtothisnode.Theaveragedegreeofanetworkisthesumofthedegreesofallnodesinthisnetworkdividedbythenumberofnodes.

Ashortestpathbetweenapairofnodesistheshortestnumberofedgesthatneedtobecrossedinorderforthetwonodestobeconnected.Theaverageshortestpathlengthistheaverageoftheshortestpathsbetweenallpairsofnodesinthenetwork.

Thesemeasureswillrevealaspectsofthestructureofyournetworkandcanbelinkedtofeaturesofthenetworkthatmightinterestyouinyourresearch:e.g.informationissharedmuchfastertoallindividualsinasocialnetworkiftheaverageshortestpathlengthislow.

WewilluseareportertocalculatetheaveragedegreeintheCodetabandthendisplayitintheInterfacetab.

AddthefollowingcodetotheCodetabattheverybottom:to-report report-av-degree let av-degree sum([count link-neighbors] of nodes) / num-nodes report av-degree end

Inthiscodewecalculatethevariableav-degreeasthesumofallnumbersofconnections([count link-neighbors] of nodes)ofallnodesdividedbythenumberofnodes(num-nodes),andwethenreportthevariableav-degreesothatwecanuseitinamonitorontheInterfacetab:

• SelectMonitorfromthedropdownbox.


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• Clickthe‘Add’button.• Clickanywhereinthewhitespace.Anewwindowwillappearwhereyoucan

determinewhatthemonitorwilldo.• Writereport-av-degreeinthe‘Reporter’box,write‘AverageDegree’inthe‘Display

Name’box,includetwodecimalplaces.ClickOK.

TocalculatetheaverageshortestpathlengthwewilluseaNetlogoextensioncalled‘nw’.InordertouseanextensioninaNetlogomodelweneedtoaddthefollowingattheverytopofthecode:

extensions [ nw ]

The‘nw’extensionneedstoknowexactlywhichsetsofagentsarethenodesandwhicharethelinks.Wehavecreatedabreedofnodesandabreedofedgesandwewillworkwiththese.Youcanspecifythisbysettingtheso-called‘context’ofthenetworkintheCodetab.Addthefollowingtothesetupprocedurejustbelowthelinecreatingthenodes:

nw:set-context nodes edges

WewillnowcreateareporterintheCodetabthatreportsanewvariableaverage-shortest-path-lengthbyusingthecommandfromthe‘nw’extensionnw:mean-path-length:

to-report average-shortest-path-length report nw:mean-path-length end

WecannowaddamonitortotheInterfacetab:


determinewhatthemonitorwilldo.• Writeaverage-shortest-path-lengthinthe‘Reporter’box,includetwodecimal

places.ClickOK.


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Nowyouwillbeabletomeasuretheaveragedegreeandaverageshortestpathlengthofanynetworkyoucreateinyourmodel.

Notethattheaverageshortestpathlengthmonitorwillsometimesreport‘false’.Thishappenswhenyournetworkhasisolatednodes,i.e.nodesthatarenotconnectedtoanyothernodes.Itwilltypicallyoccurinrandomnetworkswithalowdensity.Insuchcases,thealgorithmcannotcalculatetheshortestpathbetweenallnodepairsbecausesomenodesarenotconnected.

The‘nw’extensionwashereusedinaverysimpleexampletoillustratehowextensionscanbeimplementedinaNetlogomodel.The‘nw’extensionoffersahugerangeofothertechniquesthatwillenableyoutoperformthemostcommonnetworksciencetasks,includingsomeofthethingswehaveimplementedmanuallyabove.Fulldocumentationfortheextensioncanbefoundhere:

https://github.com/NetLogo/NW-Extension

Advancedtask:innetworkswithisolatednodesyoucouldstillcalculatetheaverageshortestpathlengthofallnodesthatareconnectedinthelargestsingleconnectedcomponent,bycreatingasubsetofnodesthatonlyincludesthenodesinlargestconnectedcomponentandcalculatingtheaverageshortestpathlengthfortheseonly.Giveitatry!UsetheNetlogodictionaryandthe‘nw’extensiondocumentation.

Saveyourmodel!

13. TradingpotsonanetworkWhenperformingappliednetworkscienceresearch,youarenotjustinterestedincreatingacertainnetworkstructurebutratherinunderstandingwhatitsconsequencesarewithinyourresearchcontext.Whatisenabledbytherelationships?Whataretheprocessestakingplaceontherelationships?Theflowofmaterialsorideas?Howdoesthestructureofthenetworkinfluencethisflow?Doesitleadtoparticularpattern,likedistributionsofmaterials


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ortherapidspreadofanidea?Theseareagainquestionsthatyouneedtoaskyourselfattheoutsetandanswerinlightofyourresearchcontext.

Inthissectionwewillintroduceaverysimpleresearchcontextandprocess:tradeandthedistributionofpotsoveranetwork.

Wewillassumeallournodesaretradersinvolvedinthetradeofpottery,andtheyareabletotradewitheachotheriftheyareconnectedinthenetwork.Wewillgivealltradersacertainamountofpotsandeverytick(Netlogojargonfortimestep)allpotsinthemodelwillbeconsideredfortrade.Tokeepitsimple,wewilljustassumethatalltraderswanttosellthepotstheyown,wanttoobtainnewitems,andthatatransactionissuccessfulwithacertainprobability.

First,wewillcreateavariableforthenodes(thetraders)called‘pots’byaddingthefollowingtothetopoftheCode,justbelowwherewedefinethebreeds:

nodes-own [pots]

Second,wewillgiveallnodespotsduringthesetupprocedurebyaddingthefollowingcodejustafterthecreationofnodes:

ask nodes [set pots num-pots]

Notethatwejustmentionedanewvariablecallednum-pots,soNetlogowillgiveusanerrorandwewillneedtoaddaslidertocontrolthisvariableintheInterfacetab:


determinewhatthesliderwilldo.• Writenum-potsinthe‘Globalvariable’box,settheminimumto0,theincrementto

1,themaximumto100andthevalueto50.ClickOK.

Nowwhenyouclickthesetupbuttonallnodeswillbegivenasmanypotsasdefinedbythevariablenum-pots.


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Third,wewillcreateanewprocedurethatdetermineswhatprocesseswilltakeplacewhenthemodelruns.Sofarwehaverestrictedourselvestodetermininghowthemodelissetup,andnowwewilldeterminewhathappensafterthatforeverytick(timestep).

Addaprocedurecalledgobywritingatthebottomofyourcodethefollowing:to go tick end

Thecommandtickwillincreasethenumberoftimestepofthemodelbyoneeverytimethegoprocedurehappens.TousethegoprocedurewewilladdabuttonforitontheInterfacetab:


determinewhatthebuttonwilldo.• Writegointhe‘Commands’boxand‘goonce’inthe‘display’box.ClickOK.

Youhavejustaddedabuttonthatwillrunthegoprocedureonceeverytimeyouclickit.Ifyoudoso,youwillnoticethatthenumberofticksintheInterfacewindowwillincreasebyoneeachtime.Youmightalsowanttocreateasecondbuttonthatrunsthegoprocedurecontinuouslyuntilyouaskittostop:


determinewhatthebuttonwilldo.• Writegointhe‘Commands’boxand‘go’inthe‘display’box.Makesurethe‘Forever’

boxisticked.ClickOK.

Youhavenowcreatedabuttonthatwillcontinuouslyrunthegoprocedure.


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Fourth,wewillstartaddingmoreinterestingtrade-relatedcommandstothegoprocedure,beginningwithacountofthetotalnumberofpotsduringanyonetick.Inthismodelthissumwillbethesameforeverytickwithinasinglesetup,butwewilladdthissumincaseyoudecidetomodifythemodelbyallowingpotstobeaddedorremovedfromthemodel.Writethefollowinginthegoprocedurebeforetick:

let total-pots sum [pots] of nodes

Fifth,nowthatweknowhowmanypotsthereareinthistickwecanrepeattradeasmanytimesastherearepotsbyaddingthefollowingcodeinthegoprocedureimmediatelyafterthesumofallpots:

repeat total-pots [ ]

Everycommandthatwenowaddwithinthesebracketswillberepeatedasmanytimesastherearepotsatthestartofthattick.

Sixth,wewillrandomlyselectanodewhichhasatleastonepotandisconnectedtoatleastoneothernode,i.e.anodethatcantrade:

repeat total-pots [ ask one-of nodes with [pots > 0 and count link-neighbors > 0] [] ]

Seventh,wewillaskthisnodetoperformatransaction(sellapottoanothernodeitisconnectedto)withacertainprobability.Wewillusethesametechniqueasweusedearlierforimplementingprobability:checkingwhetherarandomlyselectednumberishigherorlowerthanavariablerepresentingthetradeprobability.Addthefollowingtotheaskcommandwejustwrote:

ask one-of nodes with [pots > 0 and count link-neighbors > 0] [if random-float 1 < trade-probability [] ]

Thiscodewillperformanactiononlyifarandomlyselectedfloatingpointnumberbetween0and1issmallerthanthevaluewesetforthevariabletrade-probability.Let’screateasliderforthisnewvariableintheInterfacetab:


determinewhatthesliderwilldo.• Writetrade-probabilityinthe‘Globalvariable’box,settheminimumto0,the

incrementto0.05,themaximumto1andthedefaultvalueto0.5.ClickOK.


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Finally,wewilladdthetransactionthatwilltakeplaceifarandomlyselectednumberislowerthanthethresholddeterminedbythetrade-probabilityvariable.Addthefollowingtotheifcommandwejustwrote:

[if random-float 1 < trade-probability [set pots pots - 1 ask one-of link-neighbors [set pots pots + 1] ] ]

Thiscodewillperformatransactionbyfirstreducingthenumberofpotsoftheseller(therandomlyselectednode),thenitwillrandomlyselectoneoftheothernodesthisnodeisconnectedto(thissecondnodebecomesthebuyer),andfinallyitwillincreasethenumberofpotsthebuyerownsby1.

Yourcompletegoprocedureshouldnotlooklikethis:to go let total-pots sum [pots] of nodes repeat total-pots [ ask one-of nodes with [pots > 0 and count link-neighbors > 0] [if random-float 1 < trade-probability [set pots pots - 1 ask one-of link-neighbors [set pots pots + 1] ] ] ] tick end

Younowhaveamodelwhereyoucancreatearandomlyconstructednetworkwithcertainfeatures,youcanapplyalayoutalgorithmtoit,andyoucanhavethenodestradepotswitheachother.

Saveyoumodel!


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14. PlotsofpotsAtthemomentwecannotexplorethetradeprocedurewejustcreatedveryeasily,becausewedonothaveanythingthatreportsitseffects.Let’saddtwoplotsthattellussomethingaboutthenetworkandthetradeprocesses.

First,let’smakeaplotshowingthefrequencydistributionofnodes’degreesintheInterfacetab:

• SelectPlotfromthedropdownbox.• Clickthe‘Add’button.• Clickanywhereinthewhitespace.Anewwindowwillappearwhereyoucan

determinewhatthePlotwilldo.• Write‘Degreedistribution’inthe‘name’box.• Clickontheyellowpenciltomodifythe‘defaultpen’.Anewwindowwillopen

whereyoucandeterminewhatthispenwillplot.• Setthe‘Mode’dropdownboxto‘Bar’,setthe‘Interval’to1.0,andwritethe

followingcodeinthe‘Penupdatecommands’box:let max-degree max [count link-neighbors] of nodes set-plot-x-range 0 (max-degree + 1) histogram [count link-neighbors] of nodes

• ClickOKtwice.

Thisplotwillcreateahistogram,displayingthefrequencydistributionofthedegree(thenumberofedges)ofnodes.OntheXaxisweseethedegree,andontheYaxisweseethenumberofnodesthathaveacertaindegree.

Oneofthemostinterestingthingstoexplorewouldbetoseehowmanypotseachtraderhas:thedistributionofpots.WewillcreateaplotthatshowsusthisintheInterfacetab:

• SelectPlotfromthedropdownbox.• Clickthe‘Add’button.• Clickanywhereinthewhitespace.Anewwindowwillappearwhereyoucan

determinewhatthePlotwilldo.• Write‘Distributionofpots’inthe‘name’box.


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• Clickontheyellowpenciltomodifythe‘defaultpen’.Anewwindowwillopenwhereyoucandeterminewhatthispenwillplot.

• Setthe‘Mode’dropdownboxto‘Bar’,setthe‘Interval’to1.0,andwritethefollowingcodeinthe‘Penupdatecommands’box:

let max-pots max [pots] of nodes set-plot-x-range 0 (max-pots + 1) histogram [pots] of nodes

• ClickOKtwice.

Thisplotwillcreateahistogram,displayingthedistributionofpotsamongnodes.OntheXaxisweseethenumberofpots,andontheYaxisweseethenumberofnodesthatownacertainnumberofpots.

Nowyoucanstartexploringtheinterestingbehaviourofthismodel:theinteractionbetweenthenetworkstructureandthetradeprocess.

Whatshapedoesthedistributionofpotshaveforadensenetwork?Whatdoesitlooklikeforasparsenetwork?Doesthischangeoverlongtimeperiods?Howdoestheprobabilityoftradeaffectthisdistribution?

Ifyouconsidertheamountofpotsatraderhasastheirwealth,howwouldyouinterpretthesedifferentresults?Underwhatconditionsdoyouseeamoreequalwealthdistribution?Underwhatconditionsdoyouseealessequalwealthdistribution?Dothesedifferentdistributionscorrelatewithcertainnetworkstructuresasdefinedbytheaveragedegree,thedegreedistribution,andtheaverageshortestpathlength?Isthewealthofanodedependentonitspositioninthenetwork,suchasitsdegree?

Additionaladvancedexercise:Trychangingthewaynodesaregivenpots,bygivingsomenodesmorepotsthanothers,orlettingthedistributionofpotsovernodesfollowanormal,uniformorexponentialdistribution.Howdoesthisaffecttherunningofthemodel?Canyouidentifyacorrelationbetweenthenumberofpotsanodestartsoutwithinlifeandhowmanypotstheymanagetokeepandobtain?

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