On Facebook Most Ties are Weak Abstract The emergence of pervasive sociotechnical networks - PDF document

indierentnational,linguistic,ageorcommon-experiencegroups.Weaktiesareapowerfultoolfortransferringinformationacrosslargesocialdistancesandtowidesegmentsofthepopulation.Viceversa,strongtiesarecontactsbetweentrusted/knownpersons(e.g.,familytiesorclosefriendships).WeaskwhetherGranovetter'sweaktiesarealsotobefoundinOSNslikeFacebookintheformheenvisionedthem,i.e.,connectionsbetweenindividualswhobelongtodierentareasofthesocialgraph.Suchaquestion,however,ishardtoanswerforatleasttworeasons.First,Facebookismainlyorganizedaroundtherecordingofjustonetypeofrelationship:friendship.ThisimpliesthatFacebookfriendshipcaptures(andcompresses)severaldegreesandnuancesofhumanrelationshipsthatarehardtoseparateandcharacterizethroughananalysisofonlinedata.Second,asFacebookisgrowinginsizeandcomplexity,itsfriendshipnet-workisgrowingdenser,notsparser[1].AsOSNsbecomemoreandmoreinterconnected,testingGranovetter'stheoryposesseriousscalabilitychal-lenges.Earlyresearchworks[9]usedasupervisedapproach,whereapanelofFacebookuserswereaskedtoassessthestrengthoftheirownfriendshipties.Large-scalestudiesofGranovetter'stheoryinthefashionof[9]wouldarguablybeveryhardtoconduct,giventhesheersizeoftoday'sOSNs.Otherapproaches,notably[2],whichaccessedtoFacebookowndataonuseractivitiesandcomputedthetiestrengthasafunctionoftypeandfrequencyofuserinteractions.However,acut-othresholdisrequiredtodistinguishstrongtiesfromweakonesandthetuningofthatthresholdhasacrucialimpactonthecorrectidenticationofweakties.Inthisarticle,weproposeanewdenitionofweaktieswhichisrootedintheanalysisoflargeOSNsandawareofthecomputationalchallengeslyingthereof.Thestartingpointisthatinbothonlineando-linesocialnetworksparticipantstendtoorganizethemselvesintodensecommunities[8].Weproposetorstidentifycommunitieswithinthenetworkandsecondtoclassifyasweaktiesthoseedgesthatconnectuserslocatedindierentcommunities;strongtieswillbethoseedgesbetweenusersinthesamecom-munity.Wearguethatthroughourdenition,identifyingweaktiesbecomesi)fast,thankstotheeciencyofrecentalgorithmsforndingcommunitiesinlargenetworks[8]andii)robust,becausenothresholdneedstobedened.Weperformedextensiveexperimentalanalysis,thankstoapublicdatasetonFacebookfriendshipreleasedby[10]andanull-modelcomparisonagainstrandomlygeneratedgraphs.Twowell-knowncommunitydetectionalgo-rithms,namelytheLouvainMethod(LM)[3]andInfomap[19],werede-ployed.Fromtheanalysisoftheexperimentalresults,wereportthefollowingnd-ings:1.Theweak(resp.,strong)tiesdiscoveredbyLMtendtocoincidewiththosefoundbyInfomap.Importantly,ourdenitionofweaktiesis2 causeanincreaseofthedistancebetweenthem(denedasthelengthoftheshortestpathlinkingtwovertices).Thissensibledenitionis,inouropinion,morecontroversialthanitseems.First,itdependsonthenotionofshortestpathbut,unfortunately,theidenticationofall-pairsshortestpathsiscomputationallyunfeasibleevenonnetworksofmodestsize.Second,eventhealternativedenitionofdistance,i.e.,thatoflightestpath,basedonweightsassignedtoconnectionswouldremaincomputationallyprohibitiveforOSNs.Ourgoalistoexploreanovelandcomputationally-feasibledenitionofweaktiesthatsuitstheanalysisofOSNs.Insteadofarelationaldenitionthatisbasedontheintensityoftheinteractionsbetweentwousers,wepro-poseacommunity-baseddenition.Wedeneweaktiesasthoseedgesthat,afterdividingupthenetworkintocommunities(thusobtainingtheso-calledcommunitystructure),connectverticesbelongingtodierentcommunities.Finally,weclassifyintra-communityedgesasstrongties.Oneofthemostimportantfeaturesofourweaktiesisthatthosewhicharebridgescreatemore,andshorter,paths:theirdeletionwouldbemoredisruptivethantheremovalofastrongtie,fromacommunity-structureperspective.Inret-rospect,thismaybethereasonwhyweakties(albeitdenedinaslightlydierentfashion)havebeenrecentlyprovedtobeveryeectiveinthediu-sionofinformation[5,20].2.1BenetsofourdenitionOurdenitionofweaktiehasfourappealingfeatures:itisweakerthanGranovetter's,viz.thefactthatverticeslinkedbyaweaktiebelongtodierentcommunitiesdoesnotimplythattheedgebetweenthemisabridge:actually,itsdeletionmaynotdisconnectitsvertices(italmostneverdoes,inpractice).itenablestheweak/strongclassicationonthebasisoftopologicalin-formationonly.[20]alsousedtopologicalinformationbutonlylocally,i.e.,theneighborsofthetwoterminalvertices,whereasourdenitionhandlesglobalinformation,asitreliesonthepartitioningofthewholenetwork.itisbinarybecauseitlabelseachedgeinthenetworkaseitherweakorstrong.Asaconsequence,wedonotneedtotuneanythreshold,belowwhichedgesareclassiedasweak(theupshotbeingthatwecannotcomparetwoedgesonthebasisoftheirstrength).itdependsontheaccuracyofthecommunitydiscoveryphase,forwhichaccurateandscalablealgorithmsarenowavailable[8].Ourexperi-mentsshowthatourdenitionofweaktieisrobustwrt.thechoiceoftheparticularcommunitydetectionalgorithm.4 spreadofinformationandii)bothourworkand[2]areexperimentallytestedonFacebook.Viceversa,arelevantdierenceemerges:bothauthorsassignscorestoties,andclassifythemaccordingtoathresholdvalue.Incontrast,weclassifytiesasweakorstrongdependingonwhethertheyconnectverticeslocatedindierentcommunitiesornot;ourclassicationschemeisbinaryanditdoesnotusescoresandthreshold,whichmaybehardtosetupandtuneproperly.AnotherrecentapproachintheliteratureisduetoGrabowiczetal.[12].Similarlytous,theyusedinformationaboutthenetworktopologytoidentifyweakties.However,theirstudyfocusesonTwitter,whichcanbemodeledasadirectednetworkwhereuserrelationshipsaremostlyasymmetric.Pe-culiarTwitterfeatures,i.e.re-tweetandmentionhaveamajorimpactontheidenticationofweakties;therefore,ourstudyand[12]arenoteasilycomparable.4ResultsInthissectionwepresenttheresultsoftheexperimentalteststhatwecarriedouttohighlighttheprosandconsofourdenitionofweaktie.Weconsideredtwopopularmethodsfordetectingcommunities,namelytheLouvainmethod-LM[3]andInfomap[19]1.Weconsideredtwotest-beds:i)afragmentofFacebooknetworkcollectedby[10]andconsistingof957,000thousandsusersand58.4millionsfriendshipconnections.2ii)AnullmodelmadeupwithErdös-Rényirandomgraphswithanumberofverticesinthesetf128;256;512;1024;2048;4096g;theprobabilityofhavinganedgebetweenanarbitrarypairofverticesvaryinguniformlyfrom0.05to0.95.4.1RobustnessofWeakTiesDenitionAsapreliminaryexperiment,westudiedtherobustnessofourdenitionofweaktieswrt.themethodadoptedforndingcommunities.Dierentcommunitydetectionmethodsarelikelytoproduce(evenslightly)dierentresultsand,therefore,weak/strongtiesclassicationcouldvarywiththemethod.WeranbothLMandInfomaponourFacebooksampleandcommunitystructuresfoundbythetwoalgorithmswerecomparedbyapplyingtheNor-malizedMutualInformation-NMI3;NMIrangesbetween0and1andifitapproaches0thenthecommunitiesfoundbythetwoalgorithmscanberegardedastotallydissimilar. 1PleaseseetheSupplementaryMaterial:http://informatica.unime.it/weak-ties/foradetaileddescriptionofthetwomethods2ForacompletedescriptionofdatasetseetheSupplementaryMaterial.3ThedenitionofNMIisreportedintheSupplementaryMaterial.6 (a) (b)Figure3:CoverageassociatedwithErd®s-Rényi'srandomgraphs(jVj=512,plink=0:05,pinf=0:01)whenrangesfrom0to0.9.Thediagramontheleft(a)isgeneratedbyapplyingLMwhereasthediagramontheright(b)isabouttheapplicationofInfomap.4.4TheRoleofWeakTiesinInformationDiusionAsanalexperiment,westudiedhowweaktiesinuencetheinformationdiusionprocess.ThisstudyclariestheconnectionbetweenourdenitionandGranovetter'sone,whereweaktiesaredeemedtoprovidespeciclinksbetweenindividualswhowouldotherwiseremaindisconnectedastheybelongtodistantareasofthesocialgraph.Granovetter'sweaktiesshouldplayacentralroleinthespreadofinformation,butwhataboutourweakties?Howwelldotheyconveyinformation?Toassesstheirrole,weappliedtheIndependentCascadeModel(ICM)[11]tosimulatetheinformationpropagationoveragraphG.WeusedbothErd®s-Rényi'srandomgraphsandourFacebookdataset.InICM,avertexv0isselecteduniformlyatrandomtoforwardames-sagetoitsneighbors,withprobabilityequaltopinf(infectionprobability).Eachinfectedvertexcan,inturn,recursivelypropagatethemessagetoitsneighbors.Accordingto[15],reasonablevaluesofpinfare0.01,0.02and0.03.Togeneratestatisticallysignicantresults,weselectedthevertexv0tostartfrom200times;ateachselectionofv0,wesimulatedthepropagationofamessage.Wemeasuredthecoverage;denedastheratioofthenumberofverticesreceivingamessage(infectedvertices)tothetotalnumberofvertices.Theexperimentwasrepeatedbyprogressively(andrandomly)deletingafractionofweakties.Inoursimulation,rangedfrom0.1to0.9and,foreachvaluewecomputedthecorrespondingcoverage.Thewholeprocedurewasrepeatedbyreplacingweaktieswithstrongones.9 5ConclusionsInthisarticlewepresentedanoveldenitionofweaktiesdesignedforOSNslikeFacebookwhichisbasedonthecommunitystructureofthenetworkitself.Ourexperiments,carriedoutonalargeFacebooksampleandonrandomly-generatedgraphs,clearlyhighlightedtheroleandimportanceofweakties.Inparticular,wecharacterizedtheoverallstatisticaldistributionofweakties,asafunctionofthesizeofthecommunitiesandtheirdensity.Westudiedtheirroleininformationdiusionprocesses;theresultssuggestaconnectionbetweenourdenitionofweaktiesforOSNsandGranovetter'soriginalintuition.EventhoughseveralrecentworkshavefocusedontheFacebooksocialgraph[4,1],itscommunitystructure[7],andalsoonweaktiesperse[2],webelievethatourcommunity-baseddenitionofweaktiesbettertsFacebookandsimilarlylarge(anddense)OSNs.Asforfutureworks,twoprojectsmayfollowuptheresultsreportedhere.Therstistheinvestigationoftheapplicabilityofnetwork-weightingstrategiessothatthestrengthoftiescanbecomputedaccordingtoagivenrationale,forexampletheabilityofeachlinktospreadinformation.Todoso,weintendtoadoptanovelmethodofweightingedgessuitedforOSNswedevisedin[6].Thesecondinterestingdevelopmentconcernstheanalysisofthegeo-graphicaldatarelatedtoFacebookusers.Thankstothemergingofdierentgraphs,e.g.,socialandgeographical,wecangetadditionalinsightsontheroleofphysicalvs.virtualdistances.AcknowledgmentsThankstoMinasGjokaformakingtheFacebookdatasetavailableandtotheanonymousreviewersfortheircarefulandconstructivecomments.References[1]L.Backstrom,P.Boldi,M.Rosa,J.Ugander,andS.Vigna.Fourdegreesofseparation.InProc.oftheACMWebScienceConference(WebSci2012),pages3342,Evanstone,Illinois,USA,2012.ACM,ACMPress.[2]E.Bakshy,I.Rosenn,C.Marlow,andL.Adamic.Theroleofsocialnetworksininformationdiusion.InProc.oftheWorldWideWebConference(WWW2012),pages519528,Lyon,France,2012.ACMPress.11 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