With the fast development of online e-commerce nowadays, online shopping has been dominating the daily life of most peoples. Meanwhile, it raises a big challenge for both buyers and sellers to identify the right products from the numerous choices (e.g., books, movies or computers) and the right customers from a large number of different buyers. This motivates the study of recommendation system which narrows down the number of products for a particular buyer according to the buyer’s preference (e.g., [9, 10, 13, 20]). One of the most popular recommendation techniques is collaborative filtering (CF) which, for a buyer, computes recommendation scores of product items by exploiting the purchasing history of many buyers. Due to the commercial importance, the recommendation system has attracted significant attentions and the state-of-the-art is now beyond purchasing history. It has been recognized that a significant source of information to improve recommendation is the influence between users of social networks. The motivation is that peoples often share in social networks the user experience of purchased products. Recently, a great effort have been put to develop advanced collaborative filtering technique with the consideration of social network influence from different perspectives and significant improvements have been reported (e.g., [4, 7, 11, 13, 17, 18]). However, the existing studies ignore a fundamental question, that is, to which extension the social network influence can help differentiate the recommended product items. Answering this question is critical in the situation that the recommended product items have similar (or identical) scores. Without a proper answer, a recommendation system has no evidence to evaluate the optimality of recommendations, for example, whether or not the recommended product items may have more difference in terms of recommendation scores by exploring influence of social networks.