Higher-Order Directed Community Detection by A Multiobjective Evolutionary Framework

Higher-order community detection in real-life networks has recently gained significant attention, because motif-based communities reflect not only higher-order mesoscale structures but also functional characteristics. However, motif-based communities detected by existing methods for directed networks often disregard edge directionality (nonreciprocal directional arcs), so they typically fail to comprehensively reveal intrinsic characteristics of higher-order topology and information flow. To address this issue, first, we model higher-order directed community detection as a biobjective optimization problem, aiming to provide high-quality and diverse compromise partitions that capture both characteristics. Second, we introduce a multiobjective genetic algorithm based on motif density and information flow (MOGA-MI) to approximate the Pareto optimal higher-order directed community partitions. On the one hand, an arc-and-motif neighbor-based genetic generator (AMN-GA) is developed to generate high-quality and diverse offspring individuals; on the other hand, a higher-order directed neighbor community modification (HD-NCM) operation is designed to further improve generated partitions by modifying easily confused nodes into more appropriate motif-neighbor communities. Finally, experimental results demonstrate that the proposed MOGA-MI outperforms state-of-the-art algorithms in terms of higher-order topology and information flow indicators while providing more diverse community information.