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This paper characterizes hierarchical clustering methods that abide by twopreviously introduced axioms -- thus, denominated admissible methods -- andproposes tractable algorithms for their implementation. We leverage the factthat, for asymmetric networks, every admissible method must be containedbetween reciprocal and nonreciprocal clustering, and describe three families ofintermediate methods. Grafting methods exchange branches between dendrogramsgenerated by different admissible methods. The convex combination familycombines admissible methods through a convex operation in the space ofdendrograms, and thirdly, the semi-reciprocal family clusters nodes that arerelated by strong cyclic influences in the network. Algorithms for thecomputation of hierarchical clusters generated by reciprocal and nonreciprocalclustering as well as the grafting, convex combination, and semi-reciprocalfamilies are derived using matrix operations in a dioid algebra. Finally, theintroduced clustering methods and algorithms are exemplified through theirapplication to a network describing the interrelation between sectors of theUnited States (U.S.) economy.

Admissible Hierarchical Clustering Methods and Algorithms for Asymmetric Networks