  Plenty of algorithms for link prediction have been proposed and were applied
to various real networks. Among these works, the weights of links are rarely
taken into account. In this paper, 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. In both the unweighted and weighted cases, the resource allocation
index performs the best. To our surprise, the weighted indices perform worse,
which reminds us of the well-known Weak Tie Theory. Further extensive
experimental study shows that the weak ties play a significant role in the link
prediction problem, and to emphasize the contribution of weak ties can
remarkably enhance the predicting accuracy.
