Table Of ContentInformation and
Influence Propagation
in Social Networks
Wei Chen
MicrosoftResearchAsia
Laks V.S. Lakshmanan
UniversityofBritishColumbia
Carlos Castillo
QatarComputingResearchInstitute
SYNTHESISLECTURESONDATAMANAGEMENT#37
M
&C Morgan &cLaypool publishers
Copyright©2014byMorgan&Claypool
InformationandInfluencePropagationinSocialNetworks
WeiChen,LaksV.S.Lakshmanan,andCarlosCastillo
www.morganclaypool.com
ISBN:9781627051156 paperback
ISBN:9781627051163 ebook
DOI10.2200/S00527ED1V01Y201308DTM037
APublicationintheMorgan&ClaypoolPublishersseries
SYNTHESISLECTURESONDATAMANAGEMENT
Lecture#37
SeriesEditor:M.TamerÖzsu,UniversityofWaterloo
SeriesISSN
SynthesisLecturesonDataManagement
Print2153-5418 Electronic2153-5426
ABSTRACT
Researchonsocialnetworkshasexplodedoverthelastdecade.Toalargeextent,thishasbeenfu-
eledbythespectaculargrowthofsocialmediaandonlinesocialnetworkingsites,whichcontinue
growing at a very fast pace, as well as by the increasing availability of very large social network
datasetsforpurposesofresearch.Arichbodyofthisresearchhasbeendevotedtotheanalysisof
thepropagationofinformation,influence,innovations,infections,practicesandcustomsthrough
networks. Can we build models to explain the way these propagations occur? How can we vali-
dateourmodelsagainstanyavailablerealdatasetsconsistingofasocialnetworkandpropagation
tracesthatoccurredinthepast?esearejustsomequestionsstudiedbyresearchersinthisarea.
Informationpropagationmodelsfindapplicationsinviralmarketing,outbreakdetection,finding
key blog posts to read in order to catch important stories, finding leaders or trendsetters, infor-
mation feed ranking, etc. A number of algorithmic problems arising in these applications have
beenabstractedandstudiedextensivelybyresearchersunderthegarbofinfluencemaximization.
is book starts with a detailed description of well-established diffusion models, includ-
ingtheindependentcascademodelandthelinearthresholdmodel,thathavebeensuccessfulat
explainingpropagationphenomena.Wedescribetheirpropertiesaswellasnumerousextensions
tothem,introducingaspectssuchascompetition,budget,andtime-criticality,amongmanyoth-
ers.Wedelvedeepintothekeyproblemofinfluencemaximization,whichselectskeyindividuals
to activate in order to influence a large fraction of a network. Influence maximization in clas-
sic diffusion models including both the independent cascade and the linear threshold models is
computationally intractable, more precisely #P-hard, and we describe several approximation al-
gorithms and scalable heuristics that have been proposed in the literature. Finally, we also deal
withkeyissuesthatneedtobetackledinordertoturnthisresearchintopractice,suchaslearning
the strength with which individuals in a network influence each other, as well as the practical
aspectsofthisresearchincludingtheavailabilityofdatasetsandsoftwaretoolsforfacilitatingre-
search.Weconcludewithadiscussionofvariousresearchproblemsthatremainopen,bothfrom
atechnicalperspectiveandfromtheviewpointoftransferringtheresultsofresearchintoindustry
strengthapplications.
KEYWORDS
socialnetworks,socialinfluence,informationandinfluencediffusion,stochasticdif-
fusion models, influence maximization, learning of propagation models, viral mar-
keting,competitiveinfluencediffusion,gametheory,computationalcomplexity,ap-
proximationalgorithms,heuristicalgorithms,scalability.
Contents
1 Introduction ....................................................... 1
1.1 SocialNetworksandSocialInfluence ..................................1
1.1.1 ExamplesofSocialNetworks ...................................1
1.1.2 ExamplesofInformationPropagation ............................2
1.2 SocialInfluenceExamples ...........................................2
1.3 SocialInfluenceAnalysisApplications .................................4
1.4 eFlipSide .....................................................5
1.5 OutlineofisBook ...............................................6
2 StochasticDiffusionModels .......................................... 9
2.1 MainProgressiveModels...........................................10
2.1.1 IndependentCascadeModel ..................................10
2.1.2 LinearresholdModel ......................................15
2.1.3 SubmodularityandMonotonicityofInfluenceSpreadFunction ......19
2.1.4 GeneralresholdModelandGeneralCascadeModel .............20
2.2 OtherRelatedModels .............................................25
2.2.1 EpidemicModels ...........................................25
2.2.2 VoterModel ...............................................29
2.2.3 MarkovRandomFieldModel .................................30
2.2.4 Percolationeory ..........................................32
3 InfluenceMaximization ............................................. 35
3.1 ComplexityofInfluenceMaximization................................36
3.2 GreedyApproachtoInfluenceMaximization...........................38
3.2.1 GreedyAlgorithmforInfluenceMaximization ....................39
3.2.2 EmpiricalEvaluationof.G;k/.................................44
3.3 ScalableInfluenceMaximization.....................................48
3.3.1 ReducingtheNumberofInfluenceSpreadEvaluations .............48
3.3.2 SpeedingUpInfluenceComputation............................51
3.3.3 OtherScalableInfluenceMaximizationSchemes ..................66
4 ExtensionstoDiffusionModelingandInfluenceMaximization ............ 67
4.1 AData-BasedApproachtoInfluenceMaximization .....................67
4.2 CompetitiveInfluenceModelingandMaximization .....................71
4.2.1 ModelExtensionsforCompetitiveInfluenceDiffusion .............72
4.2.2 MaximizationProblemsforCompetitiveInfluenceDiffusion.........75
4.2.3 EndogenousCompetition.....................................86
4.2.4 ANewFrontier–eHostPerspective..........................88
4.3 Influence,Adoption,andProfit ......................................94
4.3.1 Influencevs.Adoption .......................................95
4.3.2 Influencevs.Profit ..........................................97
4.4 OtherExtensions ................................................101
5 LearningPropagationModels ....................................... 105
5.1 BasicModels ...................................................105
5.2 ICModel ......................................................106
5.3 resholdModels................................................109
5.3.1 StaticModels .............................................111
5.3.2 DoesInfluenceRemainStatic?................................113
5.3.3 ContinuousTimeModels....................................114
5.3.4 DiscreteTimeModels ......................................115
5.3.5 AreAllObjectsEquallyInfluenceProne? .......................116
5.3.6 Algorithms ...............................................117
5.3.7 ExperimentalValidation .....................................119
5.3.8 Discussion ................................................120
6 DataandSoftwareforInformation/Influence:PropagationResearch....... 123
6.1 TypesofDatasets ................................................123
6.2 PropagationofInformation“Memes” ................................124
6.2.1 Microblogging.............................................124
6.2.2 Newspapers/blogs/etc........................................125
6.3 PropagationofOtherActions ......................................126
6.3.1 Consumption/AppraisalPlatforms.............................126
6.3.2 User-GeneratedContentSharing/Voting .......................127
6.3.3 CommunityMembershipasAction ............................127
6.3.4 Cross-ProviderData ........................................128
6.3.5 PhoneLogs ...............................................128
6.4 Network-OnlyDatasets...........................................128
6.4.1 CitationNetworks..........................................129
6.4.2 OtherNetworks ...........................................129
6.5 OtherOff-LineDatasets ..........................................129
6.6 PublishingYourOwnDatasets .....................................130
6.7 SoftwareTools ..................................................130
6.7.1 GraphSoftwareTools.......................................131
6.7.2 PropagationSoftwareTools ..................................131
6.7.3 Visualization ..............................................132
6.8 Conclusions ....................................................132
7 ConclusionandChallenges ......................................... 135
7.1 Application-SpecificChallenges ....................................135
7.1.1 ProveValueforAdvertising/Marketing .........................135
7.1.2 LearntoDesignforVirality ..................................136
7.1.3 CorrectforSamplingBiases ..................................136
7.1.4 ContributetoOtherApplications .............................137
7.2 TechnicalChallenges .............................................137
7.3 Conclusions ....................................................139
A NotationalConventions............................................ 141
Bibliography ..................................................... 143
Index ........................................................... 159
C H A P T E R 1
Introduction
In this chapter we motivate the study of influence and information propagation by providing
numerousexamples.Inaddition,weprovidesomebasicdefinitions.
1.1 SOCIALNETWORKSANDSOCIALINFLUENCE
Social networks have been studied extensively by social scientists for decades (e.g., see [Barnes,
1954,Radcliffe-Brown,1940,WassermanandFaust,1994]).Earlierstudieshavehadtoconfine
themselvestoextremelysmalldatasets.EnabledbytheInternetandsparkedbytherecentadvent
of online social networking sites such as Facebook, LinkedIn, and Tumblr, research on social
networksiswitnessinganunprecedentedgrowthduetothereadyavailabilityoflargescalesocial
network data. is has at once led to the development of many exciting applications of online
social networks and to the formulation and the subsequent study of many research questions.
A rich body of such studies has come to be classified as theanalysisofinfluenceandinformation
propagationinsocialnetworks.
Itisouraiminthisbooktooutlinesomeofthekeyconcepts,developments,andachieve-
ments in this area, as well as studying the driving applications that underlie this research and
highlightimportantchallengesthatremainopen.Forconvenienceandconsistencyofterminol-
ogy, we will use the term socialinfluenceanalysis or just influenceanalysis to indicate the analysis
ofthediffusionofinformationorinfluencethroughasocialnetwork.
1.1.1 EXAMPLESOFSOCIALNETWORKS
Byasocialnetwork,¹wemeanapossiblydirectedgraph.Asocialnetworkmaybehomogeneous,
where all nodes are of the same type, or heterogeneous, in which case the nodes fall into more
thanonetype.
Examples of homogeneous networks include the underlying graphs representing friend-
ships in basically all of the social networking platforms (e.g., the list of “friends” in Facebook),
aswellasthegraphsrepresentingco-authorshiporco-workerrelationshipsincollaborationnet-
works.
Examplesofheterogeneousnetworksincluderatingnetworksconsistingofpeopleandob-
jectssuchassongs,movies,books,etc.Suchnetworkscanbefoundinmediaappraisalandcon-
sumptionplatformssuchasLast.fmandFlixster.Here,peoplemaybeconnectedtooneanother
¹Notbeconfusedwithanonlinesocialnetworkingsite,whichisamobileorweb-basedsoftwareplatformthatallowsusersto
interactwiththeirsocialconnections.
2 1. INTRODUCTION
viafriendshiporacquaintance,whereasobjects(songs,movies,etc.)maybelinkedwithonean-
otherbymeansofsimilarityoftheirmetadata.Forexample,twosongsmaybelinkedsinceboth
are in the same genre or by the same artist. Similarly, two movies may be directed by the same
director.Inaddition,linksmaybepresentbetweenpeopleandobjectsowingtotheirratingrela-
tionship:e.g.,userSamratingaspecificmodelofNikonSLRCameraproducesalinkbetweenthe
corresponding nodes. Another example of a heterogeneous network is a scientific collaboration
networkbetweenauthors,augmentedwitharticles(thataretheresultofcollaboration),andthe
venuestheyarepublishedin.isnetworkconsistsofthreetypesofnodes—authors,articles,and
venues—andlinksbetweennodesofthesametypeaswellasbetweennodesofdifferenttypes.
In the bulk of this book, our focus will be on information propagation in homogeneous
networks.WebrieflyreturntoheterogeneousnetworksinChapter7.
1.1.2 EXAMPLESOFINFORMATIONPROPAGATION
Webeginwithsomeconcreteexamplesofpropagationsorinformationcascadesincurrentonline
socialnetworkingsites.ConsiderFacebook,whereauserSallyupdatesherstatusorwritesona
friend’swallaboutanewshowintownthatsheenjoyed.Informationaboutthisactionistypically
communicatedtoherfriends.WhensomeofSally’sfriendscommentonherupdate,thatinfor-
mation is passed on to their friends and so on. In this way, information about the action taken
bySallyhasthepotentialtopropagatetransitivelythroughthenetwork.Samposts(“tweets”)in
Twitteraboutaniftycameraheboughtwhichheishappyabout.SomeofhisfollowersonTwitter
reply to his tweet while others retweet it. In a similar fashion, viewing of movies by users tends
topropagateonFlixsterandMovieLens,informationaboutusersjoininggroupsorcommunities
tendstospreadthroughFlickr,adoptionofsongsandartistsbylistenersspreadsthroughlast.fm,
andinterestinresearchtopicspropagatesthroughscientificcollaborationnetworks.
Is there a pattern to these propagation phenomena? What can we learn from analyzing
them and how can we benefit from the results of such analysis? In this chapter, we will address
thesequestions.
1.2 SOCIALINFLUENCEEXAMPLES
Webeginwithabriefoverviewofseveralreal-lifestoriesthatmotivatethestudyofinformation
propagationinsocialnetworks.
InafamousstudypublishedintheNewEnglandJournalofMedicine,ChristakisandFowler
[2007] analyzed the medical records of about 12,000 patients. ey extracted a real offline (as
opposedtoonline)socialnetworkfromtheserecords,basedontherelationshipsbetweenthepa-
tients,includingfriendship,sibling,spouse,immediateneighbor,etc.eirgoalwastostudythe
relationshipbetweennon-infectioushealthconditions,includingobesity,andone’ssocialneigh-
bors and understand the correlation between having obese social network neighbors and being
obeseoneself.Amongotherthings,theyfoundthathavinganobesefriendmakesanindividual
171% more likely to be obese compared to a randomly chosen person. In cases of obese spouse
1.2. SOCIALINFLUENCEEXAMPLES 3
andobesesibling,thecorrespondingnumberswere37%and40%,respectively.Itistobenoted
that their study did not focus on causation but instead on correlation. Still, their study shows
havingobesesocialcontactsisagoodpredictorofobesity.
esameauthors,inaninfluentialbook[ChristakisandFowler,2011]“presentcompelling
evidence for our profound influence on one another’s tastes, health, wealth, happiness, beliefs,
even weight, as they explain how social networks form and how they operate.” As specific ex-
amples,theyarguethatbackpainspreadfromWestGermanytoEastGermanyoncetheBerlin
wallcamedown,thatsuicidespreadsthroughcommunities,thatspecificsexualpracticesspread
through friendship networks among teenagers, and political beliefs and convictions propagate
throughnetworks,theconvictionbeingmoreintensethedenserone’sconnections.
Inthebusinessarea,afamouscasedemonstratinginformationpropagationleadingtocom-
mercial success, is the Hotmail phenomenon [Hugo and Garnsey, 2002]. In the early 1990s,
Hotmail was a relatively unknown e-mail service provider. ey had a simple idea, which was
appending to the end of each mail message sent by their users the text “Join the world’s largest
e-mailservicewithMSNHotmail.http://www.hotmail.com.”ishadtheeffectofbuildingand
boostingabrand.Inamere18months,Hotmailbecamethenumberonee-mailprovider,with8
millionusers[HugoandGarnsey,2002].eunderlyingphenomenonwasthatafractionofthe
recipients of Hotmail messages were inspired by the appended message to try it for themselves.
When they sent mail to others, a fraction of them felt a similar temptation. is phenomenon
propagatedtransitivelyandsoon,adoptionofHotmailbecameviral.
Viralphenomenaofthesortdiscussedabovehavesometimeschangedlives,asintherags-
to-riches story of Ted Williams [Zafar, 2012]. He was a homeless person in Columbus, Ohio,
USA,and hadhadmanyabrushwiththe law.HewasfoundatastreetcornerinJanuary2011
whenhewasinterviewedbyajournalist.einterviewwaspostedonYouTube,includingdetails
thatWilliamswasaformervoice-overartist.Withinmonths,thevideoattracted11millionviews,
andtriggerednumerousmessagesofsupportincludingjoboffers,changinghislifeforever.
On November 16, 2011, a song from the soundtrack of a then upcoming Indian (Tamil)
movie,called“Whythiskolaveridi?”wasreleased.ByNovember21,itwasatoptrendinTwitter.
Within a week of its release, it had attracted 1.3 million views on YouTube and more than a
million “shares” on Facebook, reaching and propagating through many non-Tamil speakers. It
eventuallywentontowintheGoldAwardfromYouTubeformostviews(e.g.,58millionasof
June2012)andwasfeaturedinmainstreammediasuchasTime,BBC,andCNN.
“GangnamStyle,”aSouthKoreansongreleasedinJuly2012,becamethefirstvideotoreach
1 billion views on YouTube as of December 21, 2012. Within one year of its first release, it has
beenviewedmorethan1.745billiontimes,evensurpassingJustinBieber’s“Baby!”
e power of online information diffusion has also been utilized by citizens responding
to natural or man-made disasters. When there was a coordinated terror attack in Mumbai in
November 2008, as the events were unfolding, tweets were being sent via SMS at the rate of
about16persecond,includinginthemsuchinformationaseyewitnessaccounts,pleasforblood
4 1. INTRODUCTION
donors,locationofbloodbanksandhospitals,etc.AWikipediapagewasupinminutes,providing
astaggeringamountofdetailandextremelyfast“live”updates.AnewswireserviceMetroblogwas
setupinshortorder,containing112Flickrphotosbyajournalistgivingafirsthandaccountofthe
aftermath.AGooglemapwithmainbuildingsinvolvedintheattacks,withlinkstobackground
and news stories was immediately set up. In Vancouver, Canada, in the summer of 2011, there
were riots following the Stanley Cup final. Rioters, many of them teens, looted and destroyed
propertiesindowntown.Manyofthemwerebraggingaboutitinsocialmedia,e.g.,posingwith
Gucci bags in front of burning cars. is triggered a widespread reaction of disgust and was
leveraged in mobilizing a cleanup effort. e amount of data made available for forensics was
staggering:contrastedwith100hofVHSfootagefrom1994riots,therenowwas5000hworth
of100typesofdigitalvideoavailableforforensicanalysis.isalongwithcooperationfromthe
publicenabledthepolicetoapprehendmostoftherioters.
1.3 SOCIALINFLUENCEANALYSISAPPLICATIONS
e study of information and influence propagation has found applications in several fields, in-
cluding viral marketing, social media analytics, the spread of rumors, stories, interest, trust, re-
ferrals,theadoptionofinnovationsinorganizations,thestudyofhumanandnon-humananimal
epidemics, expert finding, behavioral targeting, feed ranking, “friends” recommendation, social
search,etc.
Among these, viral marketing or word of mouth marketing as it is otherwise called, is a
“poster”applicationofinfluenceanalysis.evisionbehindthisistoactivateasmallnumberof
“influential”individualsinasocialnetworkthroughwhichalargenumberofotherindividualscan
beinfluencedbyaviralpropagation.Formally,considerasocialnetworkrepresentedasadirected
graphG .V;E/withnodesV correspondingtoindividualsandlinksE V V representing
D (cid:26) (cid:2)
social ties. Furthermore, suppose there is a function p E (cid:140)0;1(cid:141) that associates a weight or
W !
probabilityp.u;v/witheverylink.u;v/,representingtheinfluenceexertedbyuseruonv.is
informally captures the intuition that whenever u performs an action, then v also performs the
actionafteru,withprobabilityp.u;v/.eideabehindviralmarketingisthatbygettingasmall
set of users in V (a seed set) to use a product, for instance by giving it to them for free or at
a discounted price, we can reach a much larger set of users through transitive propagation of
influence.
Interestingly,afamilyofapplicationsinseeminglydifferentdomainsandsettingsfallintoa
patternsimilartotheonewedescribeforviralmarketing.Considerthewaterdistributionnetwork
of a large metropolitan city [Leskovec et al., 2007, Ostfeld and Salomons, 2004, Ostfeld et al.,
2006]: accidental or deliberate interference can introduce viruses or other contaminants in the
water being distributed. ere are sensors capable of detecting any outbreak, but each sensor is
expensive both in itself and in terms of its deployment and maintenance. A natural question is
whetherwecanfindasmallsetofcrucialjunctionsinthewaterdistributionnetworkinwhichto
