evaluation of node position based on mutual interaction in social network of internet users

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EvaluationofNodePositionBasedonMutualInteractioninSocialNetworkofInternetUsersPrzemysławKazienko1,KatarzynaMusiał1,AleksanderZgrzywa1Abstract:Averyinterestingscientificproblemistheassessmentofthenodepositionwithinthedirected,weightedgraphthatrepresentsthesocialnetworkofInternetusers.Theweightsofgrapharcsareextractedfromthedataaboutusermutualcommunicationorcommonactivities.Thenewmethodofnodepositionanalysis,whichtakesintoaccountboththestrengthoftheconnectionsbetweennetworknodesanddynamicofthisstrengthispresentedinthepaper.Theresultsofexperimentsonemaildatasetweredescribedaswell.Keywords:nodepositionassessment,socialnetworkofInternetusers,socialnetworkanalysis1.IntroductionThevariouskindsofe-commerceande-businesssolutionsthatexistinthemarketencouragedtheuserstoutilizetheInternetandavailableweb-basedservicesmorewillinglyintheireverydaylife.Manycustomerslookforservicesandgoodsthathavehighquality.Thus,notonlytheinformationprovidedbyvendorsisimpor-tantforpotentialcustomersbutalsotheopinionsofotheruserswhohavealreadyboughtthegoodsorusedtheparticularservice.Itisnaturalthatusers,togatherotherpeopleopinions,communicatewitheachotherviadifferentcommunicationchannels,e.g.byexchangingemails,commentingonforums,usinginstantmes-sengers,etc.ThisinformationflowfromoneindividualtoanotheristhebasisforthesocialnetworkofInternetusers(SNIU).Thisnetworkcanberepresentedasadirectedgraph,inwhichnodesaretheusersandtheedgesdescribetheinforma-tionflowfromoneusertoanother.Oneofthemostmeaningfulandusefulissueinsocialnetworkanalysisistheevaluationofthenodepositionwithinthenetwork.Sincethesocialnetworkdescribestheinteractionsbetweenpeople,theproblemofassessmentthenodepositionbecomesverycomplexbecausehumanswiththeirspontaneousandsocialbehaviorarehardpredictable.However,theeffortshouldbemadetoevaluatetheirstatusbecausesuchanalysiswouldhelptofinduserswhoarethemostinfluentialamongcommunitymembers,possessthehighestso-cialstatementandprobablythehighestleveloftrust(Golbeck,Hendler,2004),(Rana,Hinze,2004).Theseuserscanberepresentativesoftheentirecommunity.Asmallgroupofkeypersonscaninitiatenewkindsofactions,spreadnewservicesoractivateothernetworkmembers(Kazienko,Musiał,2007).Ontheotherhand,1IntituteofAppliedInformatics,WroclawUniversityofTechnology,Wyb.Wyspianskiego27,50-370Wroclaw,Polande-mail:{kazienko,katarzyna.musial,aleksander.zgrzywa}@pwr.wroc.pl 266P.Kazienko,K.Musiał,A.ZgrzywaFigure1.Aregularsocialnetworkuserswiththelowestpositionshouldbestimulatedforgreateractivityorbetreatedasthemass,targetreceiversforthepriorpreparedservicesthatdonotrequirethehighlevelofinvolvement.InordertocalculatethepositionoftheInternetuser,thenewmeasurecallednodepositionisintroducedinthefurthersections.ItenablestoestimatehowvaluabletheparticularnodewithintheSNIUis.IncontrarytothePageRankalgorithmthatisdesignedtoassesstheimportanceofthewebpages,thepresentednodepositionmeasuretakeintoaccountnotonlythesignificanceofthedirectconnectionsofanodebutalsothequalityoftheconnection.2.RelatedWorkThemainconceptofaregularsocialnetwork(Figure1)appearstobesimpleasitcanbedescribedasafinitesetofnodesthatarelinkedwithoneormoreedges(Garton,Haythorntwaite,Wellman,1997),(Hanneman,Riddle,2005),(Wasser-man,Faust,1994).Anodeofthenetworkisusuallydefinedasanactor,anindividual,corporate,collectivesocialunit(Wasserman,Faust,1994),orcustomer(Yang,Dia,Cheng,Lin,2006)whereasanedgenamedalsoatieorrelationship,asalinkagebetweenapairofnodes(Wasserman,Faust,1994).Therangeandtypeoftheedgecanbeextensive(Hanneman,Riddle,2005),(Wasserman,Faust,1994)anddifferentdependingonthetypeandcharacteroftheanalyzedactors.Thenotationthatiswidelyusedtorepresentasocialnetworkisthegraphtheory.Thenodesofagraphareactorswhileedgescorrespondtotherelationsinthesocialnetwork(Wasserman,Faust,1994).ThesocialnetworksofInternetuserssome-whatdifferfromtheregularonesandbecauseofthattheyyieldfornewapproachestotheirdefinitionandanalysis.SNIUisalsocalledanonlinesocialnetwork(Gar-ton,Haythorntwaite,Wellman,1997),computer-supportedsocialnetwork(Well-man,Salaff,1996),webcommunity(Gibson,Kleinberg,Raghavan,1998),(Flake,Lawrence,LeeGiles,2000),orweb-basedsocialnetwork(Golbeck,2005).NotethatthereisnoonecoherentdefinitionofSNIU.Someresearchersclaimthatawebcommunitycanalsobeasetofwebpagesrelevanttothesame,commontopic(Gibson,Kleinberg,Raghavan,1998),(Flake,Lawrence,LeeGiles,2000).AdamicandAdararguethatawebpagemustberelatedtothephysicalindividualinor- EvaluationofNodePositionBasedonMutualInteractioninSocialNetworkofInternetUsers267dertobetreatedasanodeintheonlinesocialnetwork.Thus,theyanalyzethelinksbetweenusers’homepagesandformavirtualcommunitybasedonthisdata.Additionally,theequivalentsocialnetworkcanalsobecreatedfromanemailcom-municationsystem(Adamic,Adar,2003).Othersdeclarethatcomputer-supportedsocialnetworkappearswhenacomputernetworkconnectspeopleororganizations(Garton,Haythorntwaite,Wellman,1997),(Wellman,Salaff,1996).Ontheotherhand,Golbeckassertstheviewthataweb-basedsocialnetworkmustfulfilthefollowingcriteria:usersmustexplicitlyestablishtheirrelationshipswithothers,thesystemmusthaveexplicitsupportformakingconnections,relationshipsmustbevisibleandbrowsable(Golbeck,2005).Socialnetworkanalysis(Wasserman,Faust,1994)providessomemeasuresuse-fultoassessthenodepositionwithinthesocialnetwork.Tothemostcommonlyusedbelong:centrality,prestige,reachability,andconnectivity(Hanneman,Rid-dle,2005),(Wasserman,Faust,1994).Thereexistmanyapproachestoevaluationofpersoncentrality(Freeman,1979):degreecentrality,closenesscentrality,andbetweenesscentrality.Degreecentralitytakesintoaccountthenumberofneigh-borsthatareadjacentfromthegivenperson(Hanneman,Riddle,2005).Theclosenesscentralitypinpointshowcloseanindividualistoalltheotherswithinthesocialnetwork(Bavelas,1950).Ittightlydependsontheshortestpathsfromthegivenusertoallotherpeopleinthesocialnetwork.Thesimilarideawasstudiedforhypertextsystems(Botafogo,Rivlin,Shneiderman,1992).Finallythebetwee-nesscentralityofamemberspecifiestowhatextendthismemberisbetweenothermembersinthesocialnetwork(Freeman,1979).Memberaismoreimportant(in-between)iftherearemanypeopleinthesocialnetworkthatmustcommunicatewithainordertomakerelationshipswithothernetworkmembers(Hanneman,Riddle,2005).Thesecondfeaturethatcharacterizesanindividualinthesocialnetworkandenablestoidentifythemostpowerfulmembersisprestige.Prestigecanbealsocalculatedinvariousways,e.g.degreeprestige,proximityprestige,andrankprestige.Thedegreeprestigetakesintoaccountthenumberofusersthatareadjacenttoaparticularuserofthecommunity(Wasserman,Faust,1994).Proximityprestigeshowshowcloseareallotheruserswithinthesocialcommunitytothegivenone(Wasserman,Faust,1994).Therankprestige(Wasserman,Faust,1994),ismeasuredbasedonthestatusofusersinthenetworkanddependsnotonlyongeodesicdistanceandnumberofrelationships,butalsoonthestatusofusersconnectedwiththeuser(Katz,1953).3.EvaluationofNodePositionBasedonMutualInteractioninSocialNetworkofInternetUsersBeforethenewmethodfornodepositionmeasurementwillbepresentedthedefi-nitionofsocialnetworkoftheInternetusersshouldbeestablished.3.1.SocialNetworkofInternetUsersThevariouskindsofdefinitionsofthesocialnetworkofInternetusers(seeSection2)yieldsforthecreationofoneconsistentapproach. 268P.Kazienko,K.Musiał,A.ZgrzywaFigure2.TwosocialnetworksofInternetusersDefinition1.SocialnetworkofInternetusersisatupleSNIU=(IID,R),whereIIDisafinitesetofnon-anonymousinternetidentitiesi.e.thedigitalrepresenta-tionofaperson,organizationalunit,groupofpeople,orothersocialentity,thatcommunicatewithoneanotherorparticipateincommonactivities,e.g.usingemailsystem,blogs,instantmessengers.Risafinitesetofinternetrelationshipsthatjoinpairsofdistinctinternetidentities:R:IID£IID,i.e.R=f(iidi;iidj):iidi2IID;iidj2IID;i6=jgand(iidi;iidj)6=(iidj;iidi).ThesetofinternetidentitiesIIDmustnotcontainisolatedmembers–withnorelationshipsandcard(IID)>1.TheexampleoftwoseparatesocialnetworkofInternetusersispresentedinFigure2.NotethatanindividualhumancansimultaneouslybelongtomanysocialnetworksintheInternet.Moreover,theycanalsomaintainseveralInternetIDs–seepersondinFigure2.Theinternetidentityisadigitalrepresentationofthephysicalsocialentity.Theseareobjectsthatcanbeunambiguouslyascribedtooneperson(individualidentity),toagroupofpeopleoranorganization(groupidentity).Thisrepresentationmustexplicitlyidentifythesocialentity(auser,groupofusersoranorganization).Thismappingenablestodefinetheconnectionsbetweensocialentitiesbasedontherelationshipsbetweentheirinternetidentities.Anindividualidentitypossessesindividuals,whereasagroupidentitycorrespondstoagroupofpeople,e.g.familythatuseonlyonelogintothefamilyblog,aswellastoanorganization,e.g.allemployeesuseonee-mailaccounttorespondcustomers’requests.Suchgroupidentitiescanbyidentifiedbycontentanalysis.Arelationshipconnectstwointernetidentitiesbasedontheircommonactivities.Everysocialentitythatisrepresentedbytheinternetidentitycanbeconsciousofsuchrelationshipornot,dependingontheprofileofactivities.Threekindsofsocialrelationshipscanbedistinguished:Directrelationship–itconnectstwo EvaluationofNodePositionBasedonMutualInteractioninSocialNetworkofInternetUsers269internetidentitieswithadirectconnector.Thedirectconnectorisanobjectthatisaddressedtothespecifictypeofinternetidentitiesandrelatedcommunication,e.g.emailaddresses(internetidentities)areconnectedwithmessagesexchangedamongthem.Thus,thedirectconnectorcanbeemailcommunication,phonecalls(orVoIP),etc.Quasi–directrelationship–twointernetidentitiesareawareofthefactthattheyareintherelationshipbuttheydonotmaintaintherelationship,e.g.peoplewhocommentonthesameblog.Indirectrelationship–theinternetidentityisnotawareofthefactthatissimilartootherinternetidentity.Twointernetidentitiesareconnectedbyindirectrelationshipwhentheirprofilesaresimilar,e.g.peoplewhoexamineandsimilarlyratethesamephotospublishedintheInternet.TheexamplesofSNIUbasedontheestablisheddefinitionare:asetofpeoplewhodateusinganonlinedatingsystem(Boyd,2004),agroupofpeoplewhoarelinkedtooneanotherbyhyperlinksontheirhomepages(Adamic,Adar,2003),thecompanystaffthatcommunicatewithoneanotherviaemail(Culotta,Bekkerman,McCallum,2004),(Shetty,Adibi,2005),etc.3.2.NodePositionEvaluationBasedonthedataderivedfromthesourcesystem,wecanbuildagraphthatrepresentstheconnectionsbetweenusersandthenanalyzethepositionofeachnodewithinsuchnetwork.NodesofthegraphrepresenttheInternetuserswhointeract,cooperateorsharecommonactivitieswithintheweb-basedsystemswhileedgescorrespondtotherelationshipsextractedfromthedataabouttheircommoncommunicationoractivities.NodepositionfunctionNP(a)ofnodearespectsboththevalueofnodepositionsofnode’saconnectionsaswellastheircontributioninactivityinrelationtoa,inthefollowingway:NP(a)=(1¡")+"¢(NP(b1)¢C(b1!a)+:::+NP(bm)¢C(bm!a))(1)where:"–theconstantcoefficientfromtherange[0;1].Thevalueof"denotestheopennessofnodepositiononexternalinfluences:howmucha’snodepositionismorestatic(small")ormoreinfluencedbyothers(greater");b1,...,bm–acquain-tancesofa,i.e.nodesthatareinthedirectrelationtoa;m–thenumberofa’sacquaintances;C(b1!a),...,C(bm!a)–thefunctionthatdenotesthecontribu-tioninactivityofb1,...,bmdirectedtoa.Ingeneral,thegreaternodepositiononepossessesthemorevaluablethismemberisfortheentirecommunity.Itisoftenthecasethatweonlyneedtoextractthehighlyimportantpersons,i.e.withthegreatestnodeposition.Suchpeoplesurelyhavethebiggestinfluenceonothers.Asaresult,wecanfocusouractivitieslikeadvertisingormarketingsolelyonthemandwewouldexpectthattheywouldentailtheiracquaintances.Thenodepositionofanodeisinheritedfromothersbutthelevelofinheritancedependsontheactivityoftheusersdirectedtothisperson,i.e.intensityofcommoninteraction,coopera-tionorcommunication.Thus,thenodepositiondependsalsoonthenumberandqualityofrelationships.Tocalculatethenodepositionofthepersonwithinthesocialnetworktheconvergent,iterativealgorithmisused.Thismeansthattherehavetobeafixedappropriatestopcondition¿. 270P.Kazienko,K.Musiał,A.ZgrzywaFigure3.ExampleofthesocialnetworkofInternetuserswiththeassignedcom-mitmentvalues3.3.CommitmentFunctionThecommitmentfunctionC(b!a)isaveryimportantelementintheprocessofnodepositionassessment,thusitneedstobeexplainedmoredetailed.C(b!a)reflectsthestrengthoftheconnectionfromnodebtoa.Inotherwords,itdenotesthepartofb’sactivitythatispassedtoa.ThevalueofcommitmentfunctionC(b!a)inSNIU(IID,R)mustsatisfythefollowingsetofcriteria:1.Thevalueofcommitmentisfromtherange[0;1]:8(a;b2IID)C(b!a)2[0;1].2.Commitmentfunctiontoitselfequals0:8(a2IID)C(a!a)=0.3.Thesumofallcommitmentshastoequal1,separatelyforeachnodeofthenetwork:X8(a2IID)=1(2)a2IID4.IfthereisnorelationshipfrombtoathenC(b!a)=0.5.Ifamemberbisnotactivetoanybodyandothernmembersai,i=1,...,nareactivetob,theninordertosatisfycriterion3,thesum1isdistributedequallyamongalltheb’sacquaintancesai,i.e.8(a2IID)C(b!ai)=1=n.Theexam-pleofnetworkofInternetuserswithvaluesofcommitmentfunctionassignedtoeveryedgeispresentedinFigure3.Accordingtotheabovecriteriaallvaluesofcommitmentarefromtherange[0;1](criterion1)aswellasthesumofallcom-mitmentsequals1,separatelyforeachuserofthenetwork(criterion3).Moreover,thevalueofcommitmentfunctionC(a!a)equals0(criterion2)andbecausethereisnorelationshipbtoasoC(b!a)=0(criterion4).Notealsothatac-cordingtocondition5,nodecisnotactivetoanybodybuttwoothersbanddareactivetoc,thuscommitmentofcisdistributedequallyamongallc’sconnectionsC(c!b)=C(c!d)=1=2. EvaluationofNodePositionBasedonMutualInteractioninSocialNetworkofInternetUsers271ThecommitmentfunctionC(a!b)ofmemberawithinactivityoftheirac-quaintancebcanbeevaluatedasthenormalizedsumofallcontacts,cooperation,andcommunicationsfromatobinrelationtoallactivitiesofa:A(a!b)C(a!b)=Pm(3)j=1A(a!bj)where:A(a!b)–thefunctionthatdenotestheactivityofnodeadirectedtonodeb,e.g.numberofemailssentbyatob;m–thenumberofallnodeswithintheSNIU.Intheaboveformulathetimeisnotconsidered.ThesimilarapproachisutilizedbyValverdeetal.tocalculatethestrengthofrelationships.Itisestablishedasthenumberofemailssentbyonepersontoanotherperson(Valverde,Theraulaz,Gautrais,Fourcassie,Sole,2006).However,theauthorsdonotrespectthegeneralactivityofthegivenindividual.Intheproposedapproach,thisgeneral,localactivityexistsintheformofdenominatorinformula3.InanotherversionofcommitmentfunctionC(a!b)allmember’sactivitiesareconsideredwithrespecttotheirtime.Theentiretimefromthefirsttothelastactivityofanymemberisdividedintokperiods.Forinstance,asingleperiodcanbeamonth.Activitiesineachperiodareconsideredseparatelyforeachindividual:Pk¡1ii=0(¸)Ai(a!b)C(a!b)=PmPk¡1i(4)j=1i=0(¸)Ai(a!bj)where:i–theindexoftheperiod:forthemostrecentperiodi=0,forthepreviousone:i=1,...,fortheearliesti=k¡1;Ai(a!b)–thefunctionthatdenotestheactivitylevelofnodeadirectedtonodebintheithtimeperiod,e.g.numberofemailssentbyatobintheithperiod;(¸)i–theexponentialfunctionthatdenotestheweightoftheithtimeperiod,¸2(0;1];k–thenumberoftimeperiods.Theactivityofnodeaiscalculatedineverytimeperiodandafterthattheappropriateweightsareassignedtotheparticulartimeperiods,using(¸)ifactor.Themostrecentperiod(¸)i=(¸)0=1,forthepreviousone(¸)i=(¸)1=(¸)isnotgreaterthan1,andfortheearliestperiod(¸)i=(¸)k¡1receivesthesmallestvalue.Theinasensesimilarideawasusedinthepersonalizedsystemstoweakenolderactivitiesofrecentusers(Kazienko,Adamski,2007).Oneoftheactivitytypesisthecommunicationviaemailorinstantmessenger.Inthiscase,Ai(a!b)isthenumberofemailsthataresentfromatobinthePmparticularperiodi;andj=1Ai(a!bj)isthenumberofallemailssentbyaintheithperiod.Ifnodeasentmanyemailstobincomparisontothenumberofalla’ssentemails,thenbhasgreatercommitmentwithinactivitiesofa,i.e.C(a!b)willhavegreatervalueandinconsequencenodepositionofnodebwillgrow.However,notalloftheelementscanbecalculatedinsuchasimpleway.Othertypesofactivitiesaremuchmorecomplex,e.g.commentsonforumsorblogs.Eachforumconsistsofmanythreadswherepeoplecansubmittheircomments.Inthiscase,Ai(a!b)isthenumberofusera’scommentsinthethreadsinwhichbhasalsoPmcommented,inperiodi,whereastheexpressionj=1Ai(a!bj)isthenumberofcommentsthathavebeenmadebyallothersonthreadswhereaalsocommented,inperiodi. 272P.Kazienko,K.Musiał,A.ZgrzywaTable1.ThestatisticalinformationfortheEnrondatasetNoofemailsbeforecleansing517,431Period(aftercleansing)01.1999-07.2002No.ofremoveddistinct,bademailaddresses3,769No.ofemailsaftercleansing411,869No.ofinternalemails(senderandrecipientfromtheEnrondomain)311,438No.ofexternalemails(senderorrecipientoutsidetheEnrondomain)120,180No.ofdistinct,cleansedemailaddresses74,878No.ofisolatedusers9,390No.ofdistinct,cleansedemailaddressesfromtheEnrondomain(socialnetworkusers)withoutisolatedmembersthesetIIDinSNIU=(IID,R)20,750No.ofnetworkuserswithinIIDwithnoactivity15,690(76%)Percentageofallpossiblerelationships5.83%4.CaseStudyTheexperimentsthatillustratetheideaofnodepositionassessmentwerecarriedoutontheEnrondataset,whichconsistsoftheemployees’mailboxes.EnronCor-porationwasthebiggestenergycompanyintheUSA.Itemployedaround21,000peoplebeforeitsbankruptcyattheendof2001.AnumberofotherresearcheshavebeenconductedontheEnronemaildataset(Priebey,Conroy,Marchette,Park,2005),(Shetty,Adibi,2005).First,thedatahastobecleansedbyremovalofbadandunificationofduplicatedemailaddresses.Additionally,onlyemailsfromwithintheEnrondomainwereleft.Everyemailwithmorethanonerecipientwastreatedas1=nofaregularemail,wherenisthenumberofitsrecipients.ThegeneralstatisticsrelatedtotheprocesseddatasetarepresentedinTable1.Afterdatapreparationthecommitmentfunctioniscalculatedforeachpairofmembers.ToevaluaterelationshipcommitmentfunctionC(a!b)bothofthepresentedformulas–3and4-wereused.Formula3wasutilizedtocalculatenodepositionwithoutrespectingtime(NP)whereasformula4servestoevaluatenodepositionwithtimefactor(NPwTF).Theinitialnodepositionsforallmemberswereestab-lishedto1andthestopconditionwasasfollows¿=0:00001.Thenodepositionswithoutandwithtimecoefficientwerecalculatedforsix,differentvaluesofthe"coefficient,i.e."=0:01,"=0:1,"=0:3,"=0:5,"=0:7,"=0:9.Theconductedcasestudyrevealedthatthetimenecessarytocalculatethenodepositionsforalluserstightlydependsonthe"value,i.e.thegreater"isthegreaterprocessingtimeis(Figure4).Thesimilarinfluencehasthevalueof"coefficientonthenumberofiterationsrequiredtofulfillthestopcondition.SomeadditionalinformationaboutthevaluesofnodepositionsprovidestheaveragenodepositionwithintheSNIU EvaluationofNodePositionBasedonMutualInteractioninSocialNetworkofInternetUsers273Figure4.Thenumberofnecessaryiterationsandprocessingtimeinrelationto"Figure5.AverageNPandNPwTF,standarddeviationofNPandNPwTF,meansquarederrorbetweenNPandNPwTFcalculatedfordifferentvaluesof"andthestandarddeviationofbothnodepositionvaluesNPandNPwTF(Figure5).Theaveragenodepositiondoesnotdependonthevalueof".Inallcases,itequalsaround1(Figure5).Itsconvergenceto1isformallyproved.However,thestandarddeviationdiffersdependingonthecoefficient"value.Thegreater"is,thebiggerstandarddeviationis.Itshowsthatforgreater"thevalueofthedistancebetweenthemembers’nodepositionsincreases,andthiscanbenoticedforbothNPandNPwTF.ItcanbenoticedthatthevalueofnodepositionNPforover93%(seealsoTable2)andNPwTFforover95%(seealsoTable3)ofthecommunityislessthan1(seealsoTable2).Itmeansthatonlyfewmembersexceedtheaveragevaluethatequals1.ThisconfirmsthatnodepositioncanbethegoodmeasuretoextractthekeyusersinSNIU(Kazienko,Musiał,2007).ThecomparisonofthevaluesofNPandNPwTF(Figure6)revealsthatmoreusersobtainhigherNPwTFpositionthanNP.ItmeansthatpeoplewhohavegreaterNPwTFweremoreactiveinthelatestperiods.NodepositionNPdenotesthegeneralpositionofanodere-gardlessoftime.Hence,NPwillbethesameforapersonathatreceivednemails 274P.Kazienko,K.Musiał,A.ZgrzywaTable2.ThepercentagecontributionofmembersintheEnronsocialnetworkwithNP¸1andNPwheretimefactorisnotincludedinrelationto""0.010.10.30.50.70.9NP¸16.9736.9736.1885.4942.2510.906NP<193.02793.02793.81294.50697.74999.094Table3.ThepercentagecontributionofmembersintheEnronsocialnetworkwithNPwTF¸1andNPwTFwheretimefactorisnotincludedinrelationto""0.010.10.30.50.70.9NPwTF¸15.8654.7234.4434.3714.1730.906NPwTF<195.13595.27795.55795.62995.82799.094frombthreeyearsagoandforausercthatalsoreceivednemailsfrombbutallinthelatestmonth.SuchsituationwillnotappearduringcalculationofNPwTF.Insuchcasethepositionofnodeawillbelowerthenofthenodec,becausetheweightassignedtotheearlierperiodwillbelowerthantheweightassignedtothelatestperiod.5.ConclusionsNodepositionisameasurefortheimportanceofauserinSNIUthatreflectsthecharacteristicoftheuser’sneighbourhood.Itsvalueforagivenindividualrespectsbothnodepositionsofthenearestacquaintancesaswellastheirattentiondirectedtotheconsidereduser.Thus,theNPmeasureprovidestheopportunitytoanalyzeSNIUwithrespecttosocialbehavioursofindividuals.Nodepositioniscrucialforextractionofkeynetworkusersandcanbesuccess-fullyusedtoestablishprojectteams(Kazienko,Musiał,2007),findnewpotentialemployees,searchthepotentialconsumersforadvertisingcampaigns(Kazienko,Adamski,2007)orinrecommendersystems(Kazienko,Musiał,2006).Itcanalsobeutilizedintargetmarketingtosearchfortheappropriatetargetgroupofcus-tomers(Yang,Dia,Cheng,Lin,2006).Asaresult,somespecificproductsorservicescanbeofferedtothecarefullyselectedrepresentativesofthenetwork,whoarethemostimportantinthepopulationaswellasthosewhopotentiallyhavethegreatestinfluenceonothers.AcknowledgementsThisworkwaspartlysupportedbyThePolishMinistryofScienceandHigherEducation,grantno.N51603731/3708. EvaluationofNodePositionBasedonMutualInteractioninSocialNetworkofInternetUsers275Figure6.ThepercentagecontributionofmemberswithNP¸NPwTFandNP