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Group Fairness Metrics for Community Detection Methods in Social Networks

Elze de Vink, Akrati Saxena

TL;DR

This work proposes group fairness metrics ($\Phi^{F*}_{p}$) to evaluate CD methods from a fairness perspective and conducts a comparative analysis of existing CD methods, focusing on the performance-fairness trade-off, to determine whether certain methods favor specific types of communities based on their size, density, or conductance.

Abstract

Understanding community structure has played an essential role in explaining network evolution, as nodes join communities which connect further to form large-scale complex networks. In real-world networks, nodes are often organized into communities based on ethnicity, gender, race, or wealth, leading to structural biases and inequalities. Community detection (CD) methods use network structure and nodes' attributes to identify communities, and can produce biased outcomes if they fail to account for structural inequalities, especially affecting minority groups. In this work, we propose group fairness metrics ($Φ^{F*}_{p}$) to evaluate CD methods from a fairness perspective. We also conduct a comparative analysis of existing CD methods, focusing on the performance-fairness trade-off, to determine whether certain methods favor specific types of communities based on their size, density, or conductance. Our findings reveal that the trade-off varies significantly across methods, with no specific type of method consistently outperforming others. The proposed metrics and insights will help develop and evaluate fair and high performing CD methods.

Group Fairness Metrics for Community Detection Methods in Social Networks

TL;DR

This work proposes group fairness metrics () to evaluate CD methods from a fairness perspective and conducts a comparative analysis of existing CD methods, focusing on the performance-fairness trade-off, to determine whether certain methods favor specific types of communities based on their size, density, or conductance.

Abstract

Understanding community structure has played an essential role in explaining network evolution, as nodes join communities which connect further to form large-scale complex networks. In real-world networks, nodes are often organized into communities based on ethnicity, gender, race, or wealth, leading to structural biases and inequalities. Community detection (CD) methods use network structure and nodes' attributes to identify communities, and can produce biased outcomes if they fail to account for structural inequalities, especially affecting minority groups. In this work, we propose group fairness metrics () to evaluate CD methods from a fairness perspective. We also conduct a comparative analysis of existing CD methods, focusing on the performance-fairness trade-off, to determine whether certain methods favor specific types of communities based on their size, density, or conductance. Our findings reveal that the trade-off varies significantly across methods, with no specific type of method consistently outperforming others. The proposed metrics and insights will help develop and evaluate fair and high performing CD methods.
Paper Structure (16 sections, 1 equation, 7 figures, 2 tables)

This paper contains 16 sections, 1 equation, 7 figures, 2 tables.

Table of Contents

  1. Introduction
  2. The Proposed Group Fairness Metric ($\Phi$)
  3. Community Mapping
  4. Community-wise Fairness Metrics
  5. Group Fairness Metric ($\Phi$)
  6. Metric Behavior
  7. Experimental Setup
  8. Community Detection Methods
  9. Datasets
  10. Results
  11. Group Fairness-Performance trade-off versus Community Size
  12. Fairness Performance trade-off vs. Community Density
  13. Fairness Performance trade-off vs. Community Conductance
  14. Fairness Metric versus Other Quality Evaluation Metrics
  15. Fairness Analysis on Real-world Networks
  16. ...and 1 more sections

Figures (7)

  • Figure 1: FCCN vs. normalized community size for each community on a dummy network. The best fit line shows the trend of a CD method.
  • Figure 2: Analyzing behavior of community-wise fairness metric and group fairness on a network having minority and majority community.
  • Figure 3: NMI vs. fairness of community detection methods with respect to community size for LFR networks of 10,000 nodes having different $\mu$ values.
  • Figure 4: NMI vs. fairness with respect to community densities on LFR networks.
  • Figure 5: NMI vs. fairness with respect to conductance on LFR networks.
  • ...and 2 more figures