MOUFLON: multi-group modularity-based fairness-aware community detection

Abstract In this paper, we propose MOUFLON, a fairness-aware, modularity-based community detection method that allows adjusting the importance of partition quality over fairness outcomes. MOUFLON uses a novel proportional balance fairness metric, providing consistent and comparable fairness scores across multi-group and imbalanced network settings. We evaluate our method under both synthetic and real-world network datasets, focusing primarily on performance and the trade-off between modularity and fairness in the resulting communities, along with the impact of network characteristics such as size, density, and group distribution. As structural biases can lead to strong alignment between demographic groups and network structure, we also examine scenarios with highly clustered homogeneous groups, to understand how such structures influence fairness outcomes. Finally, we benchmark our method against existing fairness-aware community detection approaches, and apply MOUFLON to register-derived population networks from two Swedish municipalities, demonstrating that proportionally balanced communities can be recovered at a small cost in modularity in real-world settings. Our findings showcase the effects of incorporating fairness constraints into modularity-based community detection, and highlight key considerations for designing and benchmarking fairness-aware social network analysis methods.