Gene fusion is an important evolutionary process. It can yield valuable information to infer the interactions and functions of proteins. Fused genes have been identified as non-transitive patterns of similarity in triplets of genes. To be computationally tractable, this approach usually imposes an a priori distinction between a dataset in which fused genes are searched for, and a dataset that may have provided genetic material for fusion. This reduces the genetic space in which fusion can be discovered, as only a subset of triplets of genes is investigated. Moreover, this approach may have a high-false-positive rate, and it does not identify gene families descending from a common fusion event.