The Linked Open Data community publishes an increasing number of data sources on the so-called Data Web and interlinks them to support data integration applications. We investigate how the composition of existing links and mappings can help discovering new links and mappings between LOD sources. Often there will be many alternatives for composition so that the problem arises which paths can provide the best linking results with the least computation effort. We therefore investigate different methods to select and combine the most suitable mapping paths. We also propose an approach for selecting and composing individual links instead of entire mappings. We comparatively evaluate the methods on several real-world linking problems from the LOD cloud. The results show the high value of reusing and composing existing links as well as the high effectiveness of our methods.