# Measuring group fairness in community detection

## TL;DR

This paper introduces new fairness metrics to evaluate how fairly community detection algorithms treat different groups in networks.

## Contribution

The novel contribution is a set of group fairness metrics for community detection and an analysis of fairness-performance trade-offs.

## Key findings

- Fairness-performance trade-off varies widely across community detection methods.
- Infomap and Significance methods perform well and are fair across most networks.
- No single method excels in both performance and fairness consistently.

## Abstract

Understanding community structures is crucial for analyzing networks, as nodes join communities that collectively shape large-scale networks. In real-world settings, the formation of communities is often impacted by several social factors, such as ethnicity, gender, wealth, or other attributes. These factors may introduce structural inequalities; for instance, real-world networks can have a few majority groups and many minority groups. Community detection algorithms, which identify communities based on network topology, may generate unfair outcomes if they fail to account for existing structural inequalities, particularly affecting underrepresented groups. In this work, we propose a set of novel group fairness metrics to assess the fairness of community detection methods. Additionally, we conduct a comparative evaluation of the most common community detection methods, analyzing the trade-off between performance and fairness. Experiments are performed on synthetic networks generated using LFR, ABCD, and HICH-BA benchmark models, as well as on real-world networks. Our results demonstrate that the fairness-performance trade-off varies widely across methods, with no single class of approaches consistently excelling in both aspects. We observe that Infomap and Significance methods are high-performing and fair with respect to different types of communities across most networks. The proposed metrics and findings provide valuable insights for designing fair and effective community detection algorithms.