Modularity-Fair Deep Community Detection with Multi-valued Sensitive Attributes

Detecting meaningful communities in networks is essential for understanding complex social, biological, and information systems. Modularity effectively captures the quality of communities by comparing the observed and expected edge densities, but it often overlooks fairness with regards to the connectivity of different groups of nodes within the communities. In this work, we address this limitation by proposing fairness-aware community detection algorithms that incorporate group-sensitive connectivity into the modularity framework. Our approach is based on optimizing distinct sub-matrices of the modularity matrix that isolate intra-group and inter-group connections. We introduce two algorith-mic families: (a) Input-based methods, including fair spectral and deep learning algorithms that directly operate on these sub-matrices; and (b) Loss-based methods , which integrate fairness-aware sub-matrix information into the learning objective of deep community detection models. The proposed approach is applicable to both binary and multi-valued sensitive attributes. Our experiments on synthetic and real-world networks demonstrate that our algorithms significantly improve group connectivity fairness with controlled trade-offs in modularity.