Abstract
Plenty of algorithms for link prediction have been proposed and were applied to various real networks. Among these algorithms, the weights of links are rarely taken into account. In this letter, we use local similarity indices to estimate the likelihood of the existence of links in weighted networks, including Common Neighbor, Adamic-Adar Index, Resource Allocation Index, and their weighted versions. We have tested the prediction accuracy on real social, technological and biological networks. Overall speaking, the resource allocation index performs best. To our surprise, sometimes the weighted indices perform even worse than the unweighted indices, which reminds us of the well-known Weak-Ties Theory. Further experimental study shows that the weak ties play a significant role in the link prediction, and to emphasize the contributions of weak ties can remarkably enhance the prediction accuracy for some networks. We give a semi-quantitative explanation based on the motif analysis. This letter provides a start point for the possible weak-ties theory in information retrieval.