This paper introduces hierarchical quasi-clustering methods, a generalization of hierarchical clustering for asymmetric networks where the output structure preserves the asymmetry of the input data. We first show that this output structure is equivalent to a finite quasi-ultrametric space. We then study admissibility with respect to two desirable properties and show that a modified version of single linkage is the only admissible quasi-clustering method. The application of this method is illustrated through a real-world network describing internal migration within the United States.