# Relative Hausdorff Distance for Network Analysis

arXiv: https://arxiv.org/abs/1906.04936 · HTML: https://mlsanity.com/paper/1906.04936/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jun 2019.

## Built on by (most cited first, 3 of 3)

- [A Review of Topological Data Analysis for Cybersecurity](https://mlsanity.com/paper/2202.08037/) (2022)
- [Pieceformer: Similarity-Driven Knowledge Transfer via Scalable Graph Transformer in VLSI](https://mlsanity.com/paper/2506.15907/) (2025)
- [ProHD: Projection-Based Hausdorff Distance Approximation](https://mlsanity.com/paper/2511.18207/) (2025)

## Abstract (arXiv)

Similarity measures are used extensively in machine learning and data science algorithms. The newly proposed graph Relative Hausdorff (RH) distance is a lightweight yet nuanced similarity measure for quantifying the closeness of two graphs. In this work we study the effectiveness of RH distance as a tool for detecting anomalies in time-evolving graph sequences. We apply RH to cyber data with given red team events, as well to synthetically generated sequences of graphs with planted attacks. In our experiments, the performance of RH distance is at times comparable, and sometimes superior, to graph edit distance in detecting anomalous phenomena. Our results suggest that in appropriate contexts, RH distance has advantages over more computationally intensive similarity measures.