FairRARI: A Plug and Play Framework for Fairness-Aware PageRank

TL;DR

FairRARI addresses fairness in PageRank by casting PR as a variational problem and enforcing group-fairness via a convex constraint set, solved with a simple, convergent fixed-point scheme that mirrors standard PR updates. The framework supports multiple fairness notions (φ-sum, α-min, and their combination) with linear-time projections, ensuring a target fairness level without sacrificing the original PR’s asymptotic efficiency. Theoretical results prove convergence to a unique fair PR solution and demonstrate that FairRARI outperforms post-processing baselines in preserving graph structure while achieving fairness. Empirical results across 22 real-world graphs show significant utility gains and reliable fairness across 2- and 4-group settings, establishing FairRARI as a practical and scalable tool for fairness-aware graph centrality.

Abstract

PageRank (PR) is a fundamental algorithm in graph machine learning tasks. Owing to the increasing importance of algorithmic fairness, we consider the problem of computing PR vectors subject to various group-fairness criteria based on sensitive attributes of the vertices. At present, principled algorithms for this problem are lacking - some cannot guarantee that a target fairness level is achieved, while others do not feature optimality guarantees. In order to overcome these shortcomings, we put forth a unified in-processing convex optimization framework, termed FairRARI, for tackling different group-fairness criteria in a ``plug and play'' fashion. Leveraging a variational formulation of PR, the framework computes fair PR vectors by solving a strongly convex optimization problem with fairness constraints, thereby ensuring that a target fairness level is achieved. We further introduce three different fairness criteria which can be efficiently tackled using FairRARI to compute fair PR vectors with the same asymptotic time-complexity as the original PR algorithm. Extensive experiments on real-world datasets showcase that FairRARI outperforms existing methods in terms of utility, while achieving the desired fairness levels across multiple vertex groups; thereby highlighting its effectiveness.

Figures (19)

• Figure 1: Standard PageRank (PR) and fair PR vectors under $\phi$-fairness tsioutsiouliklis2021fairness with two vertex groups (red/blue) on the PolBooks dataset. Vertex size is proportional to the PR score produced by each method. Black circles indicate vertices with zero PR score. The standard PR vector (a) assigns $\phi^\text{red}_\mathrm{o}\! =\! 0.47$ of the total PR mass to the red group. The target for the fair PR vectors is $\phi^\text{red}\! =\! 0.9$ of total mass for the red group. While both fair PR vectors in (b) and (c) attain this target, $37/49 \approx 75\%$ of blue vertices in (b) are set to zero, while $0\%$ of the blue vertices suffer such an undesirable outcome for FairRARI (c).
• Figure 2: Comparing Fair PR solutions of prior methods and FairRARI (Ours), on different datasets for $\phi$-sum-fairness with $2$ groups. The figures showcase the TV utility of each solution for different fairness levels $\phi$ (lower the better). Vertical dotted lines: $\phi_\mathrm{o}$.
• Figure 3: Comparing Fair PR solutions of prior methods and FairRARI (Ours), on different datasets with $2$ groups. The figures showcase the Kendall Tau coefficient of each solution for different fairness levels $\phi$ (higher the better). Vertical dotted lines: $\phi_\mathrm{o}$.
• Figure 4: Showcasing the TV of the FairRARI solutions for different fairness levels $\phi$, on Twitch datasets with $4$ groups. The dashed lines represent the post-processing solution for each dataset.
• Figure 5: Showcasing the TV of FairRARI and Post-Processing solutions on the $\boldsymbol{\phi}$-sum + $\boldsymbol{\alpha}$-min-fair problem.

Theorems & Definitions (19)

• Proposition 3.1
• Theorem 3.2
• Theorem 3.3
• Theorem 4.1
• Theorem 4.2
• Theorem 4.3
• Theorem 5.1
• Corollary 5.2
• Theorem 1.1
• Theorem 2.1