# Relative Hausdorff Distance for Network Analysis

## TL;DR

This paper introduces the graph Relative Hausdorff (RH) distance as a lightweight, effective similarity measure for network analysis, particularly in anomaly detection within evolving graph sequences, showing competitive performance to more complex methods.

## Contribution

The paper presents the RH distance as a novel, computationally efficient graph similarity measure and demonstrates its effectiveness in detecting anomalies in dynamic networks.

## Key findings

- RH distance performs comparably to graph edit distance in anomaly detection.
- RH distance can be more computationally efficient than traditional measures.
- Effective in both real cyber data and synthetic graph sequences.

## Abstract

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.