# Hierarchical Clustering of Asymmetric Networks

arXiv: https://arxiv.org/abs/1607.06294 · HTML: https://mlsanity.com/paper/1607.06294/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jul 2016.

## Built on by (most cited first, 5 of 5)

- [Untrained Graph Neural Networks for Denoising](https://mlsanity.com/paper/2109.11700/) (2021)
- [Hypergraphs with Edge-Dependent Vertex Weights: Spectral Clustering based on the 1-Laplacian](https://mlsanity.com/paper/2305.00462/) (2023)
- [Robust Hierarchical Clustering for Directed Networks: An Axiomatic Approach](https://mlsanity.com/paper/2108.07247/) (2021)
- [Monitoring the Dynamic Networks of Stock Returns](https://mlsanity.com/paper/2210.16679/) (2022)
- [Constrained Hierarchical Clustering via Graph Coarsening and Optimal Cuts](https://mlsanity.com/paper/2312.04209/) (2023)

## Abstract (arXiv)

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.