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The complex network representation of systems has been widely applied across various research fields, including biology, computer science, and physics. Identifying community structures and clustering vertices in complex networks is essential for analyzing network topology, examining network features, uncovering underlying patterns, predicting links, and conducting dynamic partitioning (Huang et al., 2024).
Several community partitioning approaches have been proposed based on various strategies, including label propagation (Roghani & Bouyer, 2024), spectral analysis (Zhang et al., 2021), statistical models (Liang et al., 2025), and other methods (Al-Andoli et al., 2022; Shen et al., 2023). Most of these strategies rely on quality criteria for community detection. Many studies have treated community detection as an optimization problem, frequently applying objective functions such as modularity. Modularity remains a widely used method for analyzing community structures in complex networks (He et al., 2023; Zhao et al., 2021). However, limitations arise with these methods, especially when detecting communities below a certain scale (Luo et al., 2024; Moradi & Parsa, 2019). Combining current community discovery methods with local similarities to reweight existing edges can improve partitioning performance. Local similarities typically consider the total number of co-neighbors and symmetric similarity between vertex pairs, while differences between vertices—an important relational feature—are often ignored (Guo et al., 2024; Shen et al., 2023).
Symmetric relationships are commonly used to indicate tightness among vertices, links, or communities and to identify sub-communities. However, statistical errors in community partitioning may stem from relying solely on factors such as community scale and symmetric similarity, which can obscure vertex tendencies. DAC-HPP employed an end-to-end deep clustering framework integrating high-order proximities to enhance structural cohesiveness and attribute homogeneity (Berahmand et al., 2023). This method constructed a consensus matrix by combining diverse proximity measures and applied a deep joint clustering approach to exploit the complementary strengths of embedding and clustering. DSSC used a semi-autoencoder with a pairwise constraint matrix based on pointwise mutual information to effectively learn distinctive features (Berahmand et al., 2024). Models that overlook differences among data vertices fail to capture relationships between them accurately. Symmetric network characteristics inevitably affect internal community structures (Luo et al., 2024). Therefore, incorporating asymmetric characteristics among data vertices can more accurately and efficiently uncover community structures. Clearly, local similarities do not adequately capture vertex relationships, highlighting the need to construct directed similarity measures to enhance community partitioning in networks.