Information Diffusion in Social Networks - School of Technology and ...

Information Diffusion inSocial NetworksResearch Promotion WorkshopBESU, Shibpur15 th March 2013Amitabha BagchiComputer Science and EngineeringIIT Delhi

Online Social Networks• OSNs like Facebook and Twitter areubiquitous.• In fact some of you are probably updatingyour Facebook status even as I speak.• "Stuck in boring talk about research, think I'lltake a nap....LOL"Researchers from various disciplines arewaking up to the possibilities.

Research aspects of OSNs• Sociologists have studied human socialnetworks from the dawn of their discipline.• Physicists are interested in social networksas a complex system of interacting agents• Mathematicians see stochastic processes.• Economists apply game theoryComputer Scientists built these systems. Andwe are building the systems that can analyzethe data these systems generate.

Information diffusion on OSNsQuestion: How do particular topics or pieces ofcontent become popular on OSNs?The answer to this question is tremendouslyimportant to a variety of stakeholders:commerce, political scientists, sociologistsetc

Two aspects: Macro and MicroMicro: What are individual users doing?Macro: What are the large-scale phenomenathat are observed in this system?Synthesis: Can we deduce the nature of thelarge-scale phenomena from a knowledge ofwhat individual users are doing?

Example: The SIR modelGiven a graph G and a special vertex v thathas a certain message (rumor).• Each node is in one of three states:Susceptible, Infected, Removed. Initial v isInfected and everyone else is Susceptible.• At each time step an edge (u,v) is chosen atrandom and if u is infected it sends themessage to v.• If v is S, it becomes I. If it is I it becomes R.• If v is R then u becomes R.

SIR: The Macro questionClearly, as long as there are infected nodes theprocess continues.Question: Will all the nodes have beeninfected for at least some time before theprocess ends?Ans: (Probably) depends on the topology. Fora complete graph the answer is no (Sudbury,J. Appl. Prob., 1985).

The way of PhysicsObserve the macro and theorize about themicro to better understand the universe.

The way of EngineeringUse the observation of the micro and the theoryof the micro to build better systems and makemore money......thereby helping pay for Physics research

Outline• Refine the micro question.• Define a stochastic model of the micro.• Simulate and observe the behaviour of themacro.• Compare with data.

Refining the questionThe Attribution problem: Why do users dowhat they do?• Did you share that photo because you likewhat's in it or because you are a big fan ofthe person who posted it?• You just heard on TV that Sehwag has beencut from the Indian team. Do you want toshare your opinion on Twitter?• Everyone is talking about Kolaveri. Do youwant to check it out?

Building the modelThe model comes from (possible) answers tothe questions.• People are influenced by what their friendsare talking about. (Endogenous).• People monitor broadcast media also andoften respond to it on OSNs. (Exogenous).• People respond to themes that are gettingpopular on OSNs. (Somewhere in between).

The Model I• Users form a network that is an undirectedsmall-world.• Each user “tweets” from time to time. A“tweet” is an event in time that has a “topic”associated with it.• The users options of topics at time t are froma set of topics that have been seen until timet.• The user differentiates between “global”topics and “local” topics.

The Model II• There is a “global list” in which “global tweets”arrive with frequency λ 1 (distributed as aPoisson point process). Each of these bringsa new topic.• Each user has a “local list” into which tweetsare written with frequency λ 2 (distributed as aPoisson point process).The topic of a user’s tweet is chosen randomlyout of the topics in the global list and the locallists of its neighbours in the network.

The Model III• Each global tweet has a weight A on arrival inthe global list.• This weight decreases exponentially withtime with parameter α i.e. Ae -αt at time t if thetopic arrived at time 0.• When a user tweets then that tweet is placedin its local list with weight B.• This weight decreases exponentially withtime with parameter β i.e. Be -βt at time t if thetweet arrived at time 0.

The Model IVA new tweet has two kinds of candidates it cancopy its topic from:• Global tweets.• Local tweets from one of its neighbours’ lists.A new tweet has the same topic as a candidatetweet with probability proportional to thecandidate’s weight.

A reality check• The total weight seen by any node is finitewith probability 1.• Additionally since this is an ergodic Markovprocess there is a stationary distribution,hence the total weight converges to aconstant C(v) for node v.E[C] = λ 1 A/α + kλ 2 B/β,Where k is the number of neighbors of v.

Three parameter regimesVarying the parameters gives us three kinds ofbehaviours.• Sub-viral regime: No topic dominates. Welldescribedby mean-field approximation.• Super-viral regime: Each new topic goes viraland dies quickly• Viral regime

Evolution in the viral regime800070006000Number of Nodes5000400030002000100000 100 200 300 400 500 600 700 800 900 1000timeThe simulation resembles real-world topicevolution.

Viral regime characteristics1000010000Maximum Spread1000Maximum Peak height10001001 10 100 1000Rank1001 10 100RankPower law-like distributions are seen for macroproperties like peak volume, spread andlifetime.

Live longer, go further800070006000Maximum Spread5000400030002000100000 100 200 300 400 500 600 700 800LifetimeLonger lived topics spread further. (Or is it theother way around?)

Studying topology empiricallyWe define topic based graphs for each topic• Lifetime graph: The subgraph induced by allusers who have ever tweeted on the topic.• Evolving graphs: The sequence of graphsinduced by the users who tweet on the topicon a given day.• Cumulative evolving graph: There is anedge from u to v if u follows v and u tweetson the topic a day after tweets on day t and

Topological study: Viral topicsMax Cluster Sizes/ Evolution80007000600050004000300020001000Max Cluster Size2ndmax Cluster Size3rdmax Cluster SizeEvolutionNo. of Clusters500400 450 500 550 600 650 700 750 800 850 900 950 0TimeFor a viral topic clusters merge into one as itrises in popularity. (Evolving graph)350300250200150100Number of Clusters

Topological study: Non-viral topicsMax Cluster Size / Evolution50045040035030025020015010050Max Cluster Size2ndmax Cluster Size3rdmax Cluster SizeEvolutionNo. of Clusters30025020015010050Number of Clusters0080 85 90 95 100 105 110 115 120 125TimeNon-viral topics see many small clusters.(Evolving graph)

Empirical cross-verification: Setup• We used a data set containing approx 200million tweets from 9 million users crawledfrom Twitter in 2009.• We augmented the data set by crawlingfollower-following relationships andgeolocating the users where possible.• Further we used NLP tools to tag tweets withtopics (since hashtags were very sparse).

Large cluster formation: Empirical10 210 110 3 0 10 20 30 40 50 60 70 80 0 0.050.30.4Users countPopularityGiant component0.250.20.150.1Fraction of node in Giant componentUsers count10 210 110 3 0 10 20 30 40 50 60 70 80 0 0.05PopularityGiant component0.350.30.250.20.150.1Fraction of node in Giant componentDayDayFor non-viral topics, the largest component ofthe cumulative evolving graph contains a smallfraction of all nodes

Large clusters in viral topics10 410 310 210 110 010 5 0 10 20 30 40 50 60 70 80 0 0.10.70.6Users countPopularityGiant component0.60.50.40.30.2Fraction of node in Giant componentUsers count10 410 310 210 110 5 0 10 20 30 40 50 60 70 80 0 0.1PopularityGiant component0.50.40.30.2Fraction of node in Giant componentDayDayIn viral topics the largest component takes up asignificant fraction of the graph, growing in sizeas the topic rises in popularity.

Cluster merging in the modelMax/2ndMax Cluster Size32.521.550180 85 90 95 100 105 110 115 120 125 0TimeMax/2ndMaxEvolution500450400350300250200150100EvolutionMax/2ndMax Cluster Size7000600050004000300020001000800070006000500040003000200010000400 450 500 550 600 650 700 750 800 850 900 950 0TimeMax/2ndMaxEvolutionEvolutionThe ratio of the largest to the second largestcomponent in the evolving graph tells a story.

The real data also has geography10 310 210 110 4 0 10 20 30 40 50 60 70 80 0.740.810.07Topic users countTemporalGeographical0.80.790.780.770.760.75Fraction of edges across countriesTopic users count10 110 010 2 0 10 20 30 40 50 60 70 80TemporalGeographical0.060.050.040.030.020.010Fraction of edges across countriesDayDayViral topics cross regional/national boundariesin the cumulative evolving graph.

That was the trailer…• Ruhela et. al. Towards the use of Online SocialNetworks for Efficient Internet ContentDistribution, in Proc ANTS 2011.• Ardon et. al. Spatio-Temporal Analysis of TopicPopularity in Twitter, arXiv:1111.2904v1 [cs.SI].• Rajyalakshmi et. al. Topic Diffusion andEmergence of Virality in Social Networks, arxiv:1202.2215v1 [cs.SI].www.cse.iitd.ernet.in/~bagchi

The emerging science of big data• Huge amounts of data being generated fromall kinds of sources.• “Smart cities”, Genome sequencing,telescopes, networked systme.• A growing awareness that the science of datais the new frontier of technologyThink of it as IT’s steam engine moment. It’sturn to shine as a force in human affairs.

Challenges• Modellingo Domain knowledge requiredo But understanding of what data can reveal alsorequired.• Data analyticso Algorithmso Data structureso Databaseso System Architecture

The research horizon..• …is unlimited.• Only CS fundamentals will matter.• Everything else will become obsolete beforethe exam papers are returned.

Thanks for listening