Understanding the history of a gene family that evolves through duplication, speciation, and loss is a fundamental problem in comparative genomics. Features such as function, position, and structural similarity between genes are intimately connected to this history, relationships between genes such as orthology (genes related through a speciation event) or paralogy (genes related through a duplication event) are usually correlated with these features. For example, recent work has shown that in human and mouse there is a strong connection between function and inparalogs, the paralogs that were created since the speciation event separating the human and mouse lineages. Methods exist for detecting inparalogs that either use information from only two species, or consider a set of species but rely on clustering methods. In this paper we present a graph-theoretic approach for finding lower bounds on the number of inparalogs for a given set of species, we pose an edge covering problem on the similarity graph and give an efficient 2/3-approximation as well as a faster heuristic. Since the physical position of inparalogs corresponding to recent speciations is not likely to have changed since the duplication, we also use our predictions to estimate the types of duplications that have occurred in some vertebrates and drosophila.