Recovering Fairness Directly from Modularity: a New Way for Fair Community Partitioning

TL;DR

This paper introduces a new fairness-modularity metric and an efficient algorithm for community detection that explicitly incorporates fairness, improving equitable partitioning in networks especially with unbalanced data.

Contribution

It proposes a novel fairness-modularity metric and develops the FairFN algorithm, extending traditional modularity optimization to include fairness considerations.

Findings

FairFN outperforms existing methods in fairness and partition quality.

The new metric effectively balances modularity and fairness.

Experimental results show significant improvements on unbalanced datasets.

Abstract

Community partitioning is crucial in network analysis, with modularity optimization being the prevailing technique. However, traditional modularity-based methods often overlook fairness, a critical aspect in real-world applications. To address this, we introduce protected group networks and propose a novel fairness-modularity metric. This metric extends traditional modularity by explicitly incorporating fairness, and we prove that minimizing it yields naturally fair partitions for protected groups while maintaining theoretical soundness. We develop a general optimization framework for fairness partitioning and design the efficient Fair Fast Newman (FairFN) algorithm, enhancing the Fast Newman (FN) method to optimize both modularity and fairness. Experiments show FairFN achieves significantly improved fairness and high-quality partitions compared to state-of-the-art methods, especially on unbalanced datasets.