Unbiased metrics of friends’ influence in multi-level networks

The spreading of information is of crucial importance for the modern information society. While we still receive information from mass media and other non-personalized sources, online social networks and influence of friends have become important personalized sources of information. This calls for metrics to measure the influence of users on the behavior of their friends. We demonstrate that the currently existing metrics of friends’ influence are biased by the presence of highly popular items in the data, and as a result can lead to an illusion of friends influence where there is none. We correct for this bias and develop three metrics that allow to distinguish the influence of friends from the effects of item popularity, and apply the metrics on real datasets. We use a simple network model based on the influence of friends and preferential attachment to illustrate the performance of our metrics at different levels of friends’ influence.