An essential element when analysing the structure, function, and dynamics of biological networks is the identification of communities of related nodes. An algorithm proposed recently enhances this process by clustering the links between nodes, rather than the nodes themselves, thereby allowing each node to belong to multiple overlapping or nested communities. The R package linkcomm implements this algorithm and extends it in several aspects: (i) the clustering algorithm handles networks that are weighted, directed, or both weighted and directed, (ii) several visualization methods are implemented that facilitate the representation of the link communities and their relationships, (iii) a suite of functions are included for the downstream analysis of the link communities including novel community-based measures of node centrality, (iv) the main algorithm is written in C++ and designed to handle networks of any size, and (v) several clustering methods are available for networks that can be handled in memory, and the number of communities can be adjusted by the user.