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In weighted networks, both link weight and topological structure are significant characteristics for link prediction. In this study, a general framework combining null models is proposed to quantify the impact of the topology, weight correlation and statistics on link prediction in weighted networks. Three null models for topology and weight distribution of weighted networks are presented. All the links of the original network can be divided into strong and weak ties. We can use null models to verify the strong effect of weak or strong ties. For two important statistics, we construct two null models to measure their impacts on link prediction. In our experiments, the proposed method is applied to seven empirical networks, which demonstrates that this model is universal and the impact of the topology and weight distribution of these networks in link prediction can be quantified by it. We find that in the USAir , the Celegans , the Gemo , the Lesmis and the CatCortex , the strong ties are easier to predict, but there are a few networks whose weak edges can be predicted more easily, such as the Netscience and the CScientists . It is also found that the weak ties contribute more to link prediction in the USAir , the NetScience and the CScientists , that is, the strong effect of weak ties exists in these networks. The framework we proposed is versatile, which is not only used to link prediction but also applicable to other directions in complex networks.

Quantifying the Effects of Topology and Weight for Link Prediction in Weighted Complex Networks