# FairAD: Computationally Efficient Fair Graph Clustering via Algebraic Distance

arXiv: https://arxiv.org/abs/2510.27136 · HTML: https://mlsanity.com/paper/2510.27136/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 40 references that are in the map.
- First posted on arXiv 31 Oct 2025.

## Builds on (most cited first, 14 of 14)

- [Counterfactual Fairness](https://mlsanity.com/paper/1703.06856/) (2017)
- [Certifying and removing disparate impact](https://mlsanity.com/paper/1412.3756/) (2014)
- [Fair Clustering Through Fairlets](https://mlsanity.com/paper/1802.05733/) (2018)
- [Say No to the Discrimination: Learning Fair Graph Neural Networks with Limited Sensitive Attribute Information](https://mlsanity.com/paper/2009.01454/) (2020)
- [Characteristic Functions on Graphs: Birds of a Feather, from Statistical Descriptors to Parametric Models](https://mlsanity.com/paper/2005.07959/) (2020)
- [EDITS: Modeling and Mitigating Data Bias for Graph Neural Networks](https://mlsanity.com/paper/2108.05233/) (2021)
- [Scalable Fair Clustering](https://mlsanity.com/paper/1902.03519/) (2019)
- [Guarantees for Spectral Clustering with Fairness Constraints](https://mlsanity.com/paper/1901.08668/) (2019)
- [Fair and Optimal Classification via Post-Processing](https://mlsanity.com/paper/2211.01528/) (2022)
- [Improved Approximation Algorithms for Individually Fair Clustering](https://mlsanity.com/paper/2106.14043/) (2021)
- [Unbiased Graph Embedding with Biased Graph Observations](https://mlsanity.com/paper/2110.13957/) (2021)
- [Fairness in Semi-supervised Learning: Unlabeled Data Help to Reduce Discrimination](https://mlsanity.com/paper/2009.12040/) (2020)
- [Fairness, Semi-Supervised Learning, and More: A General Framework for Clustering with Stochastic Pairwise Constraints](https://mlsanity.com/paper/2103.02013/) (2021)
- [Scalable Spectral Clustering with Group Fairness Constraints](https://mlsanity.com/paper/2210.16435/) (2022)

## Abstract (arXiv)

Due to the growing concern about unsavory behaviors of machine learning models toward certain demographic groups, the notion of 'fairness' has recently drawn much attention from the community, thereby motivating the study of fairness in graph clustering. Fair graph clustering aims to partition the set of nodes in a graph into k disjoint clusters such that the proportion of each protected group within each cluster is consistent with the proportion of that group in the entire dataset. It is, however, computationally challenging to incorporate fairness constraints into existing graph clustering algorithms, particularly for large graphs. To address this problem, we propose FairAD, a computationally efficient fair graph clustering method. It first constructs a new affinity matrix based on the notion of algebraic distance such that fairness constraints are imposed. A graph coarsening process is then performed on this affinity matrix to find representative nodes that correspond to k clusters. Finally, a constrained minimization problem is solved to obtain the solution of fair clustering. Experiment results on the modified stochastic block model and six public datasets show that FairAD can achieve fair clustering while being up to 40 times faster compared to state-of-the-art fair graph clustering algorithms.