Fair Network Communities through Group Modularity

Communities in networks are groups of nodes that are more densely connected to each other than to the rest of the network, forming clusters with strong internal relationships. When nodes have sensitive attributes, such as demographic groups in social networks, a key question is whether nodes in each group are equally well-connected within each community. We model connectivity fairness using group modularity, an adaptation of modularity that accounts for group structures. We introduce two versions of group modularity, each grounded on a different null model, and propose fairness-aware community detection algorithms. Finally, we provide experimental results on real and synthetic networks, evaluating both the connectivity fairness of community structures in networks and the performance of our fairness-aware algorithms.