  This paper considers networks where relationships between nodes are
represented by directed dissimilarities. The goal is to study methods that,
based on the dissimilarity structure, output hierarchical clusters, i.e., a
family of nested partitions indexed by a connectivity parameter. Our
construction of hierarchical clustering methods is built around the concept of
admissible methods, which are those that abide by the axioms of value - nodes
in a network with two nodes are clustered together at the maximum of the two
dissimilarities between them - and transformation - when dissimilarities are
reduced, the network may become more clustered but not less. Two particular
methods, termed reciprocal and nonreciprocal clustering, are shown to provide
upper and lower bounds in the space of admissible methods. Furthermore,
alternative clustering methodologies and axioms are considered. In particular,
modifying the axiom of value such that clustering in two-node networks occurs
at the minimum of the two dissimilarities entails the existence of a unique
admissible clustering method.
