HyFora: Hyperspherical representation and frustration quantification for community structure discovery in complex information networks

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Complex information networks encode rich associative structural information about group organization, cross-group interactions, and information diffusion, making community structure discovery an important task in information science. However, existing methods mostly rely on Euclidean proximity or local structural features, making it difficult to balance global community separation with local relational consistency measurement. To address this issue, this paper proposes HyFora , a hyperspherical frustration-aware framework for community structure discovery in complex information networks. HyFora first constructs a background-corrected relation operator to distinguish community-relevant structural deviations from degree-driven connectivity patterns. Based on this operator, node relations are represented on the unit hypersphere, where directional consistency and angular separation jointly characterize intra-community cohesion and inter-community distinction. HyFora further quantifies the mismatch between local relations and global community organization as structural frustration, providing an interpretable consistency measure for community readout and boundary-node analysis. Experimental results show that HyFora achieves maximum relative improvements of approximately 21.2%, 27.3%, 15.4%, and 14.0% in terms of NMI, ARI, ACC, and modularity Q , respectively, while ablation, sensitivity, and node-ranking analyses verify the effectiveness and interpretability of the proposed components. The source code is publicly available at .