Table Of ContentSPRINGER BRIEFS IN OPTIMIZATION
Wen Xu
Weili Wu
Optimal
Social
Influence
123
SpringerBriefs in Optimization
SeriesEditors
SergiyButenko,TexasA&MUniversity,CollegeStation,TX,USA
MirjamDür,UniversityofTrier,Trier,Germany
PanosM.Pardalos,UniversityofFlorida,Gainesville,FL,USA
JánosD.Pintér,LehighUniversity,Bethlehem,PA,USA
StephenM.Robinson,UniversityofWisconsin-Madison,Madison,WI,USA
TamásTerlaky,LehighUniversity,Bethlehem,PA,USA
MyT.Thai ,UniversityofFlorida,Gainesville,FL,USA
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Wen Xu (cid:129) Weili Wu
Optimal Social Influence
WenXu WeiliWu
DepartmentofMathematics DepartmentofComputerScience
andComputerScience UniversityofTexas,Dallas
TexasWoman’sUniversity Richardson,TX,USA
Denton,TX,USA
ISSN2190-8354 ISSN2191-575X (electronic)
SpringerBriefsinOptimization
ISBN978-3-030-37774-8 ISBN978-3-030-37775-5 (eBook)
https://doi.org/10.1007/978-3-030-37775-5
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Preface
Social computing is an emerging research field that studies the computational
aspects of social networks. Social influence specifically studies the behaviors of
individuals and the influence diffusion among them in a social network, which
involvesinterdisciplinaryfieldssuchasmathematics,sociology,psychology,com-
puterscience,business,andpublicsafety.
This book is a collection of chapters illustrating optimal social influence. It
focusesonrecentandpracticalapplications,models,algorithms,andopentopicsfor
futureresearch.Themaintopicscovercharacteristicsofsocialnetworks,modeling
of social influence propagation, popular research problems in social influence
analysis such as influence maximization, rumor blocking, rumor source detection,
and multiple social influence competing. The authors present some of the latest
social computing research and illustrate how to understand and manipulate social
influence for knowledge discovery by applying various data mining techniques in
thereal-worldscenarios.
There are a total of five chapters, which form a complete series of optimal
socialinfluence,andmeanwhile,areself-containedtoprovidethegreatestreading
flexibility. Chapter 1 introduces basic concepts on how to characterize both social
networksandsocialinfluence.Chapter2illustratesdiffusionofinfluenceinsocial
networks. Chapter 3 presents a practical application: rumor source detection in
social networks. In Chap.4, we show current research on how to block rumor
propagationefficientlyinsocialnetworks.Inthelastchapter,wefocusonmodeling
multiplesocialinfluencecompetinginanetwork.
Thetargetaudienceofthisbookincludesbutnotlimitedtoresearchers,scholars,
graduate students, and developers who are interested in social influence research.
The book also aims to serve as a textbook for graduate courses such as computa-
tionalsocialnetworks.Wegratefullyacknowledgethesupport,encouragement,and
patienceofProfessorDing-ZhuDu.
Denton,TX,USA WenXu
Dallas,TX,USA WeiliWu
October2019
v
Contents
1 IntroductionofSocialInfluenceAnalysis ................................. 1
1.1 Introduction ............................................................. 1
1.2 CharacteristicsofSocialNetworks..................................... 3
1.3 MeasuringSocialInfluence............................................. 5
1.3.1 EdgeBasedMetrics............................................. 6
1.3.2 NodeBasedMetrics ............................................ 7
1.3.3 UserBehaviorBasedMetrics.................................. 9
1.4 IdentifyingSocialInfluence ............................................ 11
1.4.1 Homophily ...................................................... 11
1.4.2 ExistentialTest.................................................. 14
1.4.3 Influence-RelatedTopics....................................... 16
1.5 Summary ................................................................ 20
2 DiffusionofInformation .................................................... 21
2.1 Introduction ............................................................. 21
2.2 ModelFormation........................................................ 22
2.2.1 EpidemicModels ............................................... 22
2.2.2 ProductAdoptionModel ...................................... 24
2.2.3 DiffusionModels ............................................... 25
2.3 ProblemOptimization .................................................. 30
2.3.1 InfluenceMaximization ........................................ 30
2.3.2 MisinformationMinimization.................................. 33
2.4 Large-ScaleDataAnalysis ............................................. 34
2.5 ResearchTrends......................................................... 34
2.5.1 LearnInfluenceProbabilitiesofDiffusionModels ........... 35
2.5.2 LearntheSpeedofInfluenceSpreadinNetworks............ 35
2.5.3 StudyVariationsofInfluenceMaximization .................. 36
vii
viii Contents
3 InformationSourceDetectioninSocialNetworks ....................... 37
3.1 Introduction ............................................................. 37
3.2 SingleSourceDetection ................................................ 40
3.2.1 ProblemFormulation........................................... 40
3.2.2 MonitorBasedApproach....................................... 42
3.2.3 ProposedAlgorithm ............................................ 44
3.2.4 Experiments..................................................... 45
3.3 DetectingMultipleRumorSourcesinNetworkswithPartial
Observations............................................................. 49
3.3.1 TheModel....................................................... 50
3.3.2 TheAlgorithm .................................................. 52
3.3.3 SimulationResults.............................................. 59
3.4 Conclusion .............................................................. 62
4 RumorBlockinginSocialNetworks....................................... 65
4.1 Overview ................................................................ 65
4.2 Community-BasedLeastCostRumorBlocking ...................... 67
4.2.1 Deterministic One-Activate-Many (DOAM)
PropagationModel.............................................. 68
4.2.2 RumorControlProblem........................................ 69
4.2.3 SetCoverBasedGreedyAlgorithmforDOAMModel ...... 70
4.2.4 ExperimentSetupandEvaluation.............................. 74
4.3 RumorBlockingMaximizationwithConstrainedTime .............. 79
4.3.1 PropagationModels ............................................ 80
4.3.2 RumorContainmentwithConstraints ......................... 82
4.3.3 PossibleSolutions .............................................. 89
4.4 Conclusion .............................................................. 90
5 MultipleSocialInfluence:ModelsandApplications..................... 93
5.1 Overview ................................................................ 93
5.2 UserBehaviorPrediction............................................... 94
5.2.1 RelatedWork.................................................... 96
5.2.2 BehaviorPredictionProblem................................... 98
5.2.3 ModelingSocialInfluenceasElectricChargedSystem ...... 99
5.2.4 Algorithms ...................................................... 104
5.2.5 Experiment...................................................... 106
5.3 Conclusion .............................................................. 114
Bibliography...................................................................... 115
Chapter 1
Introduction of Social Influence Analysis
1.1 Introduction
With the emergence and rapid proliferation of social applications and media, such
as instant messaging (e.g., WhatsApp, Viber, WeChat, Snapchat, Line, Facebook
Messenger,andGoogleHangouts),sharingsites(e.g.,Flickr,YouTube,andYelp),
blogs (e.g., WordPress and LiveJournal), wikis (e.g., Wikipedia and PBWiki),
microblogs(e.g.,TwitterandWeibo),socialnetworks(e.g.,Facebook),andcollab-
orationnetworks(e.g.,DBLP),thereislittledoubtthatsocialinfluenceisbecoming
a prevalent, complex, and subtle force that governs the dynamics of all social
networks. Therefore, social influence study has started to attract intense attention
duetomanyimportantapplications.
Socialinfluenceoccurswhenone’sopinions,emotions,orbehaviorsareaffected
by others, intentionally or unintentionally. Generally there are two alternative
models of influence resulting from behavior in response to referrals: normative
influencewhererecipientbehaviorisbasedoninterpretingtheinformationprovided
bytheinfluencer asanimpliedexpectation toconform,orinformationalinfluence
where recipient behavior is based on a personal evaluation of the information
provided by the influencer. For instance, a friend recommends strongly a new
restaurant that you have never heard of before and then you tried it. This is called
informationalsocialinfluencesinceyougetnewinformationfromothers.Another
example,allyourfriendsareusingsocialapplicationssuchasTwitterorFacebook.
Althoughyouarenotafanofsocialapplications,youstilluseittokeepconnections
withallthefriends.Thisiscallednormativesocialinfluence, whichistoconform
tothepositiveexpectationsofothers.
In the context of normative influence, the mechanisms influencing actions are
identificationandcompliance.Recipientbehaviorisdrivenbythedesiretomaintain
the relationship with the influencer and/or be associated with a referent group by
fitting in in order to evoke a favorable response from the group. The recipient’s
willingness to conform is stronger when recipient behavior is observable to the
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https://doi.org/10.1007/978-3-030-37775-5_1
2 1 IntroductionofSocialInfluenceAnalysis
influencerandtoothersinthesocialnetwork.Incontrast,themechanismunderlying
informational influence is internalization, where behavior occurs only when such
action is congruent with the recipient’s value system and by a personal evaluation
of the benefits. Such compliance involves independent information processing by
recipientswiththegoalofmaximizingoutcomesforthemselves.
Overall,behaviorslinkedtonormativeinfluencearedrivenbyrecipients’desire
to comply, and direct benefits from the action for recipients are often a secondary
consideration.Incontrast,behaviorlinkedtoinformationalinfluencearisesfroman
evaluationofthedirectbenefitstotherecipient.Whilebehaviorlinkedtonormative
influence is often discontinued when recipient action is not observable or salient
to the influencer or the group, behavior in response to informational influence is
usuallysustainedandincorporatedintohabitualactionsofrespondentsovertime.
Three Degrees of Social Influence Three degrees of influence is a theory in the
realmofsocialnetworks,proposedbyNicholasA.ChristakisandJamesH.Fowler
in2007[43].ChristakisandFowlerfoundthatsocialnetworkshavegreatinfluence
onindividuals’behavior.Butsocialinfluencedoesnotendwiththepeopletowhom
apersonisdirectlytied.Weinfluence ourfriendswhointheirturninfluence their
friends, meaning that our actions can influence people we have never met. They
positthat“everythingwedoorsaytendstoripplethroughournetwork,havingan
impact on our friends (one degree), our friends’ friends (two degrees), and even
ourfriends’friends’friends(threedegrees).Ourinfluencegraduallydissipatesand
ceases to have a noticeable effect on people beyond three degrees of separation”.
Thisargumentisbasicallythatpeereffectsneednotstopatonedegree,andthat,if
we can affect our friends, then we can (in many cases) affect our friends’ friends,
andsoon.
Studies by Christakis and Fowler suggested that a variety of attributes—like
obesity [43], smoking [44], and happiness [68]—rather than being individualistic,
arecasuallycorrelatedbycontagionmechanismsthattransmitthesebehaviorsover
longdistanceswithinsocialnetworks.Thethreedegreesofinfluencepropertyhas
alsobeenobservedincriminalnetworks[203].Thisappliestomanyaspectsoflife,
frompublichealthtoeconomics.Forinstance,itmightbepreferabletoimmunize
individualslocatedinnetwork’scentermorethanperipheralindividuals.Or,itmight
be much more effective to motivate clusters or people to avoid criminal behavior
thantoactuponindividualsorthantopunisheachcriminalseparately.
If people are connected to everyone by six degrees of separation[134] and
influence those up to three degrees [68], then people can reach halfway to anyone
in the world. The strength of social influence depends on many factors such as
thestrengthofrelationshipsbetweenpeopleinthenetworks,thenetworkdistance
between users, temporal effects, characteristics of networks and individuals in the
network.Also,nodes(users,entities)areinfluencedbyothersforvariousreasons.
Forexample,thecolleagueshavestronginfluenceonone’swork,whilethefriends
havestronginfluenceonone’sdailylife.Howtoprovetheoreticallyorempirically
that social influence does exist? How to quantify the strength of those social
1.2 CharacteristicsofSocialNetworks 3
influences? What kind of factors decides the strength of social influence in real
largenetworks?
In this chapter, we focus on computational aspect of social influence analysis
and describe the measures and algorithms related to it. In Sect.1.2, we introduce
fundamentalconceptsaboutmodelingsocialnetworks,whicharedeeplyrelatedto
theimportanceorinfluenceofnodesoredgesinthenetworks.InSects.1.3and1.4,
weaimatqualitativelyorquantitativelymeasuringtheinfluencelevelsofnodesand
edgesinthenetwork.
1.2 CharacteristicsofSocialNetworks
A clear understanding of social influence in social networks cannot be achieved
withoutaclearunderstandingofcharacteristicsofsocialnetworks.Therefore,inthis
section,wegiveanoverviewaboutsocialnetworksidentifyingitssignificanceand
characteristics. Although levels of analysis are not necessarily mutually exclusive,
therearethreegenerallevelsintowhichnetworksmayfall:micro-level,meso-level,
andmacro-level.
At the micro-level, social network analysis typically emphasizes on social
relationshipbetweensocialactorsinsteadoftheattributesofsocialactors.Itstudies
asmallgroupofindividualsinaparticularsocialcontextsuchasdyadsandtriads,
where a dyad is a social relationship between two individuals and a triad is social
relationships among three individuals. For an overview of basic social network
analysistechniques,wereferthereadertothebookbyWassermanandFaust[199].
Therearemanyinterestingpropertiesaboutsocialnetworksthathavebeenstudied
bysociologists.In1967,Milgram[134]showsthattheaveragepathlengthbetween
two Americans is six hops. By way of introduction, from any other person in the
world, so that a chain of “a friend of a friend” statements can be made to connect
anytwopeopleinamaximumofsixsteps,whichiscalled“sixdegreeofseparation”
theory.In2003,ColumbiaUniversityconductedananalogousexperimentonsocial
connectedness among Internet email users, which kind of confirmed Milgram’s
theory. In 2013 [121], Lou et al. predict reciprocity and triadic closure in social
networksbyproposingatriadfactorgraph(TriFG)model,whichincorporatessocial
theories into a semi-supervised learning method. On a large Twitter network, they
show that with the proposed factor graph model it is possible to accurately infer
90%ofreciprocalrelationshipsinadynamicnetwork.
At the meso-level, research begins with a population size that falls between
the micro- and macro-levels. As a type of complex network, social network has
somewell-knowntheoreticalpropertiessuchaspower-lawdegreedistributions,the
small-worldproperty,andthescale-freeproperty.Power-lawdistributionmeansthat
the probability that a node has degree k is proportional to k−γ, for large k and
γ > 1. The parameter γ is called the power-law coefficient. Researchers have
shown that many real-world networks are power-law networks, including power
grids[153],neuralnetworks[27],Internettopologies[61],theWeb[15,106],and
