Community Detection via Enhanced Label Propagation with Adamic-Adar Similarity and Community Size Influence

The Label Propagation Algorithm (LPA) is widely used for community detection due to its simplicity and efficiency, but its reliance on random processes often leads to unstable and fragmented communities. To address these limitations, we propose AA-LPA, a deterministic method that integrates Adamic-Adar (AA) centrality to guide label propagation. Our method introduces three key mechanisms: (1) node prioritization via AA-derived centrality to enforce stable update sequences, (2) AA-weighted label influence amplified by community size to suppress noisy edges, and (3) deterministic tie-breaking using structural centrality for reproducible results. Evaluations on real-world networks (Karate, Dolphins, Football) demonstrate that AA-LPA achieves superior alignment with ground-truth communities, attaining perfect NMI and F1 scores (1.0) in benchmark datasets, while outperforming modularity-optimizing methods (e.g., Leiden, Louvain) and stochastic LPA variants. The deterministic design ensures consistency across runs, making it particularly suitable for applications requiring interpretable and reliable community structures, such as social network analysis and functional module identification.