In this Brief Report, we propose a new index of user similarity, namely the transferring similarity, which involves all high-order similarities between users. Accordingly, we design a modified collaborative filtering algorithm, which provides remarkably higher accurate predictions than the standard collaborative filtering. More interestingly, we find that the algorithmic performance will approach its optimal value when the parameter, contained in the definition of transferring similarity, gets close to its critical value, before which the series expansion of transferring similarity is convergent and after which it is divergent. Our study is complementary to the one reported in [E. A. Leicht, P. Holme, and M. E. J. Newman, Phys. Rev. E {bf 73} 026120 (2006)], and is relevant to the missing link prediction problem.
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