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

arXiv: https://arxiv.org/abs/2305.03223 · HTML: https://mlsanity.com/paper/2305.03223/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 92 references that are in the map.
- First posted on arXiv 5 May 2023.

## Builds on (most cited first, 13 of 13)

- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Recipe for a General, Powerful, Scalable Graph Transformer](https://mlsanity.com/paper/2205.12454/) (2022)
- [Graph Neural Networks in Recommender Systems: A Survey](https://mlsanity.com/paper/2011.02260/) (2020)
- [Understanding over-squashing and bottlenecks on graphs via curvature](https://mlsanity.com/paper/2111.14522/) (2021)
- [On Over-Squashing in Message Passing Neural Networks: The Impact of Width, Depth, and Topology](https://mlsanity.com/paper/2302.02941/) (2023)
- [Understanding Oversquashing in GNNs through the Lens of Effective Resistance](https://mlsanity.com/paper/2302.06835/) (2023)
- [Oversquashing in GNNs through the lens of information contraction and graph expansion](https://mlsanity.com/paper/2208.03471/) (2022)
- [Political Discourse on Social Media: Echo Chambers, Gatekeepers, and the Price of Bipartisanship](https://mlsanity.com/paper/1801.01665/) (2018)
- [Echo Chambers: Emotional Contagion and Group Polarization on Facebook](https://mlsanity.com/paper/1607.01032/) (2016)
- [Bridging Systems: Open Problems for Countering Destructive Divisiveness across Ranking, Recommenders, and Governance](https://mlsanity.com/paper/2301.09976/) (2023)
- [Gaps in Information Access in Social Networks](https://mlsanity.com/paper/1903.02047/) (2019)
- [Reducing Access Disparities in Networks using Edge Augmentation](https://mlsanity.com/paper/2209.07616/) (2022)

## Built on by (most cited first, 4 of 4)

- [Oversmoothing, Oversquashing, Heterophily, Long-Range, and more: Demystifying Common Beliefs in Graph Machine Learning](https://mlsanity.com/paper/2505.15547/) (2025)
- [Structural Bias Beyond Homophily: A Study of Fairness in Link Prediction](https://mlsanity.com/paper/2602.11802/) (2026)
- [Estimating Fair Graphs from Graph-Stationary Data](https://mlsanity.com/paper/2510.07536/) (2025)
- [k-hop Fairness: Addressing Disparities in Graph Link Prediction Beyond First-Order Neighborhoods](https://mlsanity.com/paper/2603.03867/) (2026)

## Abstract (arXiv)

Social networks contribute to the distribution of social capital, defined as the relationships, norms of trust and reciprocity within a community or society that facilitate cooperation and collective action. Therefore, better positioned members in a social network benefit from faster access to diverse information and higher influence on information dissemination. A variety of methods have been proposed in the literature to measure social capital at an individual level. However, there is a lack of methods to quantify social capital at a group level, which is particularly important when the groups are defined on the grounds of protected attributes. To fill this gap, we propose to measure the social capital of a group of nodes by means of the effective resistance and emphasize the importance of considering the entire network topology. Grounded in spectral graph theory, we introduce three effective resistance-based measures of group social capital, namely group isolation, group diameter and group control, where the groups are defined according to the value of a protected attribute. We denote the social capital disparity among different groups in a network as structural group unfairness, and propose to mitigate it by means of a budgeted edge augmentation heuristic that systematically increases the social capital of the most disadvantaged group. In experiments on real-world networks, we uncover significant levels of structural group unfairness when using gender as the protected attribute, with females being the most disadvantaged group in comparison to males. We also illustrate how our proposed edge augmentation approach is able to not only effectively mitigate the structural group unfairness but also increase the social capital of all groups in the network.