The prediction of graph evolution is an important and challenging problem in the analysis of networks and of the Web in particular. But while the appearance of new links is part of virtually every model of Web growth, the disappearance of links has received much less attention in the literature. To fill this gap, our approach DecLiNe (an acronym for DECay of LInks in NEtworks) aims to predict link decay in networks, based on structural analysis of corresponding graph models. In analogy to the link prediction problem, we show that analysis of graph structures can help to identify indicators for superfluous links under consideration of common network models. In doing so, we introduce novel metrics that denote the likelihood of certain links in social graphs to remain in the network, and combine them with state-of-the-art machine learning methods for predicting link decay. Our methods are independent of the underlying network type, and can be applied to such diverse networks as the Web, social networks and any other structure representable as a network, and can be easily combined with case-specific content analysis and adopted for a variety of social network mining, filtering and recommendation applications. In systematic evaluations with large-scale datasets of Wikipedia we show the practical feasibility of the proposed structure-based link decay prediction algorithms.