Measuring Coverage and Divergence of Reading Behaviors Among Friends

Given data from an online friendship network (e.g., the Facebook social network) and its social reader (i.e., a reading application deployed on a social network), how can we e↵ectively capture the similarities between the reading behaviors of a user and her friends over time? Also, how can we e↵ectively summarize such similarities across users? For the first question, we are interested in measures of coverage and divergence, which are based on tie-strength functions. Coverage captures the amount by which the firstorder Markov assumption holds between the reading behaviors of user u and her friends. Divergence captures the amount of inconsistency in their reading tie-strength across time. We define reading tie-strength on a bipartite graph of users ⇥ articles, where an edge e(u, a) indicates that user u read article a. In this work, we study three popular tie-strength functions (namely, Common Neighbor, Jaccard Index, and Adamic-Adar); and propose coverage and divergence measures for the social-reader domain. In addition, we introduce a method for summarizing coverage and divergence values across all users that takes into account the heavy-tailed distribution and the sparsity of the data. Our experiments on a real-world dataset from a large media company demonstrate that Common Neighbor (i.e., number of common articles read between a user and her friend) is a better tie-strength function for the social-reader domain than Jaccard Index or Adamic-Adar.