Many statistical analyses of genetic data rely on the assumption of independence among samples. Consequently, relatedness is either modeled in the analysis or samples are removed to “clean” the data of any pairwise relatedness above a tolerated threshold. Current methods do not maximize the number of unrelated individuals retained for further analysis, and this is a needless loss of resources. We report a novel application of graph theory that identifies the maximum set of unrelated samples in any dataset given a user-defined threshold of relatedness as well as all networks of related samples. We have implemented this method into an open source program called Pedigree Reconstruction and Identification of a Maximum Unrelated Set, PRIMUS. We show that PRIMUS outperforms the three existing methods, allowing researchers to retain up to 50% more unrelated samples. A unique strength of PRIMUS is its ability to weight the maximum clique selection using additional criteria (e.g. affected status and data missingness). PRIMUS is a permanent solution to identifying the maximum number of unrelated samples for a genetic analysis.