document: Influence and correlation in social networks In many online social systems , social ties between users play an important role in dictating their behavior . One of the ways this can happen is through social influence , the phenomenon that the actions of a user can induce his\/her friends to behave in a similar way . In systems where social influence exists , ideas , modes of behavior , or new technologies can diffuse through the network like an epidemic . Therefore , identifying and understanding social influence is of tremendous interest from both analysis and design points of view . This is a difficult task in general , since there are factors such as homophily or unobserved confounding variables that can induce statistical correlation between the actions of friends in a social network . Distinguishing influence from these is essentially the problem of distinguishing correlation from causality , a notoriously hard statistical problem . In this paper we study this problem systematically . We define fairly general models that replicate the aforementioned sources of social correlation . We then propose two simple tests that can identify influence as a source of social correlation when the time series of user actions is available . We give a theoretical justification of one of the tests by proving that with high probability it succeeds in ruling out influence in a rather general model of social correlation . We also simulate our tests on a number of examples designed by randomly generating actions of nodes on a real social network ( from Flickr ) according to one of several models . Simulation results confirm that our test performs well on these data . Finally , we apply them to real tagging data on Flickr , exhibiting that while there is significant social correlation in tagging behavior on this system , this correlation can not be attributed to social influence .
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