Structural Group Unfairness: Measurement and Mitigation by means of the Effective Resistance

📄 Paper - https://arxiv.org/abs/2305.03223

• Adrian Arnaiz-Rodriguez, Georgina Curto, Nuria Oliver
• Accepted at ICWSM 2025

Overview

Social networks contribute to the distribution of social capital—relationships and norms that enable cooperation within communities. We propose three effective resistance-based metrics to quantify group social capital:

• Group Isolation
• Group Diameter
• Group Control

These metrics allow us to detect Structural Group Unfairness—disparities in access to social capital between groups. We further present a budgeted edge augmentation heuristic to reduce such disparities, improving fairness and overall network connectivity.

We provide different versions of the PyTorch code to compute Effective Resistance. More theoretical details about the behaviour of this metric can be found on the Appendix A of the paper.

Contributions

• 📐 Novel Metrics: Group-level social capital measures using effective resistance.
• 🧠 Spectral Graph Theory foundation (Effective Resistance a.k.a. Commute Time).
• ⚖️ Structural Group Unfairness definition & measurement.
• 🛠️ Mitigation Strategy: Edge addition heuristic that enhances fairness.
• 📊 Empirical Validation on real-world social networks.

Repository Structure

.
├── data/                         # Sample datasets or download scripts
├── utils/                        # Core algorithms for measurement and mitigation
|   ├── GraphWrapper.py              # Graph Object optimized for spectral computations and link additions 
|   ├── link_addition_torch.py       # Get edge scores and strongest-weakest ones
|   ├── torch_resistance_metrics.py  # Computation of metrics derived from effective resistance (Group Isolation,...)
|   ├── resistance_metrics.py        # Optimized implementation of effective resistance
|   └── {baseline}.py                # Baseline algorithms for comparison         
└── main_{baseline_}experiment.py # Main scripts to run the measurement and mitigation with diff strategies

📑 Citation

@inproceedings{arnaiz2025structural,
  title={Structural Group Unfairness: Measurement and Mitigation by means of the Effective Resistance},
  author={Arnaiz-Rodriguez, Adrian and Curto, Georgina and Oliver, Nuria},
  booktitle={Proceedings of the International Conference on Web and Social Media (ICWSM)},
  year={2025}
}

Contact

For questions, please contact: adrian@ellisalicante.org