Social and Technological Networks · Course specifics • Lectures – Tuesdays 12:10 – 13:00 • 7 Bristo Square, Lecture Theatre 2 – Fridays 12:10 – 13:00 • 1 George Square,

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!