social and technological networks · course specifics • lectures – tuesdays 12:10 – 13:00...
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SocialandTechnologicalNetworks
RikSarkar
UniversityofEdinburgh,2017.
Coursespecifics
• Lectures– Tuesdays12:10–13:00
• 7BristoSquare,LectureTheatre2– Fridays12:10–13:00
• 1GeorgeSquare,G.8GaddumLT
• Webpage– hPp://www.inf.ed.ac.uk/teaching/courses/stn/
• Lookoutforannouncementsonthewebpage
Network
• AsetofenSSesornodes:V• Asetofegdes:E– Eachedgee=(a,b)fornodesa,binV– Anedge(a,b)representsexistenceofarelaSonoralinkbetweenaandb
Networksareeverywhere
• AnyinteresSngsystemhasmanyenSSesorcomponents
• ThereexistdifferentrelaSonsbetweenthesecomponents– Thereisanetwork
• ProperSesofthenetworkdetermineproperSesofthesystem
• Inthiscourse,wewillstudyhownetworkproperSesaredefined,computedandanalyzed
Example:Socialnetworks• Facebook,Linkedin,twiPer..• Nodesarepeople• Edgesarefriendships
• Thenetworkdeterminessociety,communiSes,etc..
• HowinformaSonflowsinthesociety
• HowinnovaSon/influencespreads
• WhoaretheinfluenSalpeople• Predictbehaviour
Worldwideweb
• Links/edgesbetweenwebpages
• DeterminesavailabilityofinformaSon
• ImportantpageshavemorelinkspoinSngtothem
• Networkanalysisisthebasisofsearchengines
Computernetworks
• Whatcanwesayabouttheinternet?• Howreliablearecomputernetworks?
Electricitygrid• Networkofmanynodes,redistribuSngpower• CriScalinfrastructure• Failurecandisrupt…everything• Smalllocalfailurescanspread
– Loadredistributes– Triggeracasdadeoffailures
• NetworkstrcutureiscriScal
FromBarabasi:NetworkScience
RoadnetworkandtransportaSon• MobilitypaPernsofpeople– LocaSondata
• Failurecascades• Trafficneeds• Suggestbusroutes• Suggesttravelplans• Trafficengineering• Increasingimportance– Morevehicles– Selfdrivingcars
LinguisScnetworks
• Networksofwords• ShowsimilariSesbetweenlanguages• Showdifferencesbetweenlanguages• Documentanalysis
BusinessandmanagementandmarkeSng
• Business– Whatmakesarestaurantsuccessful?
– Nearbyrestaurants?Communityofcustomers?
• MarkeSng/management– WhoaretheinfluenSalpeopleinspreadofideas/products?
Othernetworks
• Chemistry/biology– InteracSonsbetweenchemicals– InteracSonsbetweenspecies– Ecologicalnetworks
• Finance/economies– DependenciesbetweeninsStuSons
– Resilienceandfragility• Neural(Brain)networks
WhyNetworkscience?WhyNow?• ManyofthesesystemshavesimilarunderlyingcharacterisScs
• NetworksciencestudiesthesegeneralproperSes
• Wenowhavemanytools:algorithms,graphtheory,opSmizaSon…
• Lastdecadeorsoalotofnetwork-typedatahasbecomeavailable– www–searchenginesetc– LocaSondata:trafficandroaddata
• Wecannowlookatthisdataandsearchfortheories
Networkanalysisindatascience
• Datagefngmorecomplex• ManytypesofdataarenotpointsinRdspace– DatacarryrelaSons–networks– SimpleclassificaSoninadequate– E.g.datafromsocialnetworkorsocialmedia,www,IoTandsensornetworks
Networkanalysisindatascience
• Networksreflecttheshapeofdata• Connectnearbypointswithedges• Analyseresultantnetwork
Thebreadthofnetworkscience• Tiedtorealsystems– AnythinginnetworksciencehasimpactonmulSplerealthings
• Datadriven– Needgooddata-handlingtechniques,opSmizaSons,approximaSons
– Gettolearndatadriventhinking– Studyofalgorithms,datamining
• MathemaScalandrigorous– Emphasisonpreciseunderstanding,provableproperSes.Clearthinking.
– Exactlywhatistrueandwhatisnot,whatworksandwhatdoesn’t,inexactlywhichcircumstances
Topicsofstudy• Randomgraphs:themostbasic,unstructuredsimplenetworks– WhataretheirproperSes?Whatcanweexpect?– Erdosrenyigraphs– ConstrucSonofrandomgraphs
• Powerlawandscalefreenetworks– DistribuSonofdegreesofnodes– Powerlawoccursinmanyplaces:www,socialnetsetc..
– Whatistheprocessthatgeneratesthis?Howdoweknowthatitistherightprocess?
Topicsofstudy
• Smallworldnetworks– Milgram’sexperiment– WhatisthedealwithsixdegreesofseparaSon– Howarepeoplesowellconnected?
• Webgraphsandrankingofwebpages– Google’soriginsandpagerank– HowdoyouidenSfyimportantwebpages?– Analysisofthealgorithm:dotheyconverge?Cantheygiveaclearanswer?
• Spectralmethods
Topicsofstudy
• StrongandweakSesinsocialnetworks,socialcapital– HowdoesinformaSonspreadinasocialnetwork?– HowdoyoumakeuseofyourposiSoninanetwork?– Whichcontactsareusefulinfindingjobs?Why?
• WhatarethecommuniSes(closeknitgroups)?– HowdocommuniSesaffectsocialprocesses?– Clustering/unsupervisedlearning
Topicsofstudy
• Cascades–thingsthatspread– Nodefailures– Epidemics,diseases– InnovaSon–products,ideas,technologies
• Howcanwemaximizeaspread?– WhoarethemostinfluenSalnodes?– HowcanweidenSfythem?– SubmodularopSmizaSon
Topicsofstudy
• Shapeofnetworks– Whatistheshapeofinternet?– WhatarebowSeandtree-likenetworks?– Whatdoesitmeantosayanetworkistree-like?
Thecourse
• Isnotabout:– Facebook,Whatsapp,Linkedin,TwiPer…– Makingapps
Thecourse
• Isabout:– UnderstandingmathemaScalmeasuresthatdefineproperSesofnetworks
– MathemaScsandalgorithmstocomputeandanalyzetheseproperSes
• Isnotmachinelearning– Butrelatedtoit
Ourapproach• Clearlydefinedifferentaspectsofnetworks– Whatisarandomgraph?– Whatexactlyisasmallworld?– Howdoyoudefine‘community’orclusteringinnetworks?
– HowdoyoudefineinfluenSalnodes?• Designalgorithmstoanalyzenetworks– FindcommuniSes,findinfluenSalnodes– UnderstandtheproperSesofthesealgorithms– Whendotheywork,whendotheynotwork
• Why?
Ourapproach
• TestideasonrealandarSficialnetworks– Datadrivenunderstanding– DorealnetworkshavetheproperSespredictedbytheory?
– Dothealgorithmsworkaswellasexpected?
Project• 1project.40%ofmarks• Given:AroundOct5to10.• Due:AroundNov15.• Choosefromoneofseveralprojects• Objec&ve:Trysomethingnewinnetworkscience.• Givenproblemstatement,tryyourownideasonhowtosolveit
– NouniquesoluSon.• Wewillgiveyouatopic.Youhaveto
– Formulateitasaprecisenetworkproblem– Findawaytosolveit– Youareallowedtotrydifferentproblemsandapproaches
• Submitcodeand≈3pagereport• Markedonoriginality,rigorofwork(properanalysis/experiments),
clarityofpresentaSon
Possibletypesofprojects• GivenadatasetfromaparScularsocial/technologicalarea,findawaytosolveaparScularproblem– DeviseapredicSonmethod– FindinteresSngproperSesofspecificnetworks– DesignofefficientalgorithmstocomputenetworkproperSes
• ProgrammingisusefulforevaluaSon/experiments– Wewillusepythoninclass(recommended)– Youcanuseotherlanguages(python,java,c,c++)
• TheoreScalworkisalsogreat.ButmusthaveanalyScalapproachsuchasproofs
TheoryExam
• Standardexam,60%ofmarks• Explainphenomena,devisemechanisms,proveproperSes…
• Lastyear’spaperonline..
Lectures• Slideswillbeuploadedaqereachclass• Lecturenoteswillbegivencoveringsomematerialleqover• Exerciseproblemswillbegivencoveringimportant
material• Ipython(jupyter)notebookswillbeuploaded• Dotheexerciseproblemstomakesure
– Youunderstandthings– YoucansolveanalyScproblems
• SoluSonswillbegivenlaterforimportantproblems– CheckthatyoursoluSonisright– CheckthatyourwriSngissufficientlyprecise
Pre-requisites
• Probability,distribuSons,settheory• Basicgraphtheoryandalgorithms– Graphs,trees,DFS,BFS,minimumspanningtrees,sorSng
• AsymptoScnotaSons:BigO.• Linearalgebra
• MatrixoperaSons• (preferably)Eigenvectorsandeigenvalues
• Sampleproblemsonline
CourselearningexpectaSons• Formulateproblems• Planandexecuteoriginalprojects• Useprogrammingtoanalyzenetworkdata• UsetheoreScalanalysis(maths)tounderstandideas/models
• Presentanalysisandideas– Precisely– Unambiguously– Clearly
• Havefunplayingwithideas!