MOUFLON: Multi-group Modularity-based Fairness-aware Community Detection

TL;DR

The paper tackles the problem of fairness-aware community detection in networks with multiple demographic groups, addressing imbalances that can bias partitions. It introduces MOUFLON, a scalable Louvain-based algorithm that optimizes a weighted sum $\alpha Q_P + (1-\alpha) F_P$, where $Q_P$ is modularity and $F_P$ is a novel global proportional balance fairness score. A key contribution is the proportional balance fairness framework, including the group balance $balance(C_i)$, the expected proportional balance $exp\_prop(C_i)$, the community fairness $prop\_balance(C_i)$, and the global score $F_P$, enabling tunable trade-offs between quality and fairness. Empirical results on synthetic and real networks show that proportional balance offers robust fairness across different $\alpha$ and group distributions, while modularity increases with $\alpha$ and can lead to more or fewer communities depending on structure; highly clustered homogeneous groups pose fairness challenges, underscoring the need for careful benchmarking. Overall, MOUFLON enables fair, scalable community detection in large networks and provides insights for designing fairness-aware network analysis methods and benchmarks.

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 network datasets, focusing 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. 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.

Figures (9)

• Figure 1: Example network with $V=\{1..10\}$. The set $H=\{\{1,2,7,10\},\{3,5,8,9\},\{4,6\}\}$ corresponds to the node membership in either of $K=3$ demographic groups coded as colors: blue (cross-hatch filling), red (diagonal filling) and green (dot filling)
• Figure 2: Examples of proportional balance fairness scores for various communities, rounded to two decimals. We consider the same network setting as Fig. \ref{['fig:fair-cd-example']} with $n=10$, $|H_1|=|H_2|=4, |H_3|=2, \phi=1/2$
• Figure 3: Execution time of MOUFLON, $\alpha=0.5$ (in seconds). Left panel: synthetic data (1a) with increasing network size $n$, $p=0.001$. Right panel: synthetic data (1b) with increasing network density, $n=10000$
• Figure 4: Modularity and fairness scores for the default MOUFLON (prop_balance) method on synthetic data with $p\_sensitive=0.5$, for varying $\alpha$, and number of communities (inset panels) of the identified partition. (A) Synthetic data with individual node coloring (2a). (B) Synthetic data with clique coloring (2b)
• Figure 5: Modularity and fairness scores for the default MOUFLON (prop_balance) method on synthetic data, $\alpha=0.5$, for varying $p\_sensitive$, and the number of communities (inset panels) for the identified partition. (A) Synthetic data with individual node coloring (2a). (B) Synthetic data with clique coloring (2b)