# Hierarchical Quasi-Clustering Methods for Asymmetric Networks

arXiv: https://arxiv.org/abs/1404.4655 · HTML: https://mlsanity.com/paper/1404.4655/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Apr 2014.

## Built on by (most cited first, 4 of 4)

- [An Impossibility Theorem for Node Embedding](https://mlsanity.com/paper/2105.13251/) (2021)
- [Robust Hierarchical Clustering for Directed Networks: An Axiomatic Approach](https://mlsanity.com/paper/2108.07247/) (2021)
- [An objective function for order preserving hierarchical clustering](https://mlsanity.com/paper/2109.04266/) (2021)
- [Infinity Search: Approximate Vector Search with Projections on q-Metric Spaces](https://mlsanity.com/paper/2506.06557/) (2025)

## Abstract (arXiv)

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 show that this output structure is equivalent to a finite quasi-ultrametric space and study admissibility with respect to two desirable properties. We prove that a modified version of single linkage is the only admissible quasi-clustering method. Moreover, we show stability of the proposed method and we establish invariance properties fulfilled by it. Algorithms are further developed and the value of quasi-clustering analysis is illustrated with a study of internal migration within United States.