# Influence and Correlation in Social Networks Xufei wang Nov-7-2008.

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Influence and Correlation in Social Networks Xufei wang Nov-7-2008

Background, Concepts Problem statement Basic idea Experimental Evaluation Future directions Outline 2

Proofs of social correlation People interact with others – Advices, reading, commenting – Communicating with others Non-causal correlation – Both the CO 2 level and crime level have increased sharply – Both beer and diaper sales well in a super market Causal correlation – I bought an IPhone after I’m recommended by my friend 3

Social influence A bought an IPhone after B told him it’s cool – Directed: B influences A, not A influences B – Chronological: A is influenced after B told him – Asymmetry: B has influence to A doesn’t imply A has the same influence to B 4

Social influence: One person performing an action can cause her contacts to do the same. – A bought an IPhone after B told him it’s cool Homophily: Similar individuals are more likely to become friends. – Example: two mathematicians are more likely to become friends. Confounding factors: External influence from elements in the environment. – Example: friends live in the same area, thus attend and take pictures of similar events, and tag them with similar tags. Sources of correlation 5

Background, Concepts Problem statement Basic idea Experimental Evaluation Future directions Outline 6

Social correlation and social influence are different concepts Are they related? Maybe yes and Maybe no Problem statement 7

Background, Concepts Problem statement Basic idea Experimental Evaluation Future directions Outline 8

Influence model: each agent becomes active in each time step independently with probability p(a), where a is the # of active friends. Natural choice for p(a): logistic regression function: with ln(a+1) as the explanatory variable. I.e., Coefficient α measures social correlation. Social correlation evaluation 9

Shuffle Test: – Chronological property Edge-Reversal Test: – Asymmetry property Testing for influence 10 UserABC Time123 UserABC Time231 A B C A B C

Background, Concepts Problem statement Basic idea Experimental Evaluation Future directions Outline 11

Influence model – Only use the influence factor – Current node A has “a” active friends, its probability to be active is related with the # of active friends Correlation model – Use the homophily and confounding factors – Init S nodes as centers randomly, add a ball of radius 2 to each node in S, according to the data on Flickr, randomly pick the same # of nodes to be active Experimental setup 12

Simulation results Shuffle test, influence model 13

Simulation results Edge-reversal test, influence model 14

Simulation results Shuffle test, correlation model 15

Simulation results Edge-reversal test, correlation model 16

Shuffle test on Flickr data 17

Edge-reversal test on Flickr data 18

Explanations The users’ tagging actions are independent The users either seldom visit their friends’ pages Or the users visit pages but only care about the content rather than the tags 19

Background, Concepts Problem statement Basic idea Experimental Evaluation Future directions Outline 20

Future directions I The relationship in the internet is weak! – How weak it is? So I think it’s interesting to search close communities, based on strong correlation, in blogosphere – How to define the “strongness” – How the “strongness” among the users – Do we have reasonable datasets – “strongness” is related with time? 21

Future Directions II Most of the users don’t contact frequently – How about the contact distribution Search for stable relationships is also interesting. Seeking stable communities – How to define stable? – Stable relationship can be strong or weak connection – Contact infrequently but regularly – The group can be small – Hold for a long time?? 22

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