Alternative axiomatic constructions for hierarchical clustering of asymmetric networks

The authors have introduced an axiomatic construction for hierarchical clustering of asymmetric - i.e. weighted and directed - networks. In such construction, nodes in a two-node network cluster together at the largest of the two dissimilarities. This paper introduces two alternative constructions requiring clustering at the smallest dissimilarity and being agnostic at whether the minimum or maximum is the proper choice. Within the first framework, unilateral clustering is defined and shown to be the unique method that satisfies the proposed axioms. Within the second framework, uniform bounds are established in the minimum and maximum resolution at which clusters are formed. Unilateral clustering is used to study internal migration in the United States.