Fairness-Sensitive PageRank Approximation

TL;DR

This paper introduces an efficient mean-field approximation for Fairness-Sensitive PageRank that balances influence across diverse groups in social networks, reducing computational costs while maintaining fairness.

Contribution

It develops a closed-form approximation for FSPR using node degree and group labels, enabling scalable fairness-aware ranking without costly matrix inversions.

Findings

Reduces runtime of FSPR by an order of magnitude.

Accurately estimates fairness-sensitive PageRank scores.

Enables scalable fairness-aware ranking in large networks.

Abstract

Real-world social networks have structural inequalities, including the majority and minorities, and fairness-agnostic centrality measures often amplify these inequalities by disproportionately favoring majority nodes. Fairness-Sensitive PageRank aims to balance algorithmic influence across structurally and demographically diverse groups while preserving the link-based relevance of classical PageRank. However, existing formulations require solving constrained matrix inversions that scale poorly with network size. In this work, we develop an efficient mean-field approximation for Fairness-Sensitive PageRank (FSPR) that enforces group-level fairness through an estimated teleportation (jump) vector, thereby avoiding the costly matrix inversion and iterative optimization. We derive a closed-form approximation of FSPR using the in-degree and group label of nodes, along with the global group proportion. We further analyze intra-class fluctuations by deriving expressions for the variance of approximated FSPR scores. Empirical results on real-world networks demonstrate that the proposed approximation efficiently estimates the FSPR while reducing runtime by an order of magnitude, enabling fairness-constrained ranking at scale.