Structural Embedding Representation Method (SERM): A Masked Self-Supervised Framework for Structural Embedding Learning in Complex Networks

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Complex networks are widely used to represent interactions in communication systems, biological systems, and large-scale infrastructure. Learning informative network-level representations is important for network analysis, structural similarity retrieval, and characterization of network properties. Existing representation learning methods, however, may have limited ability to jointly capture multi-hop topological dependencies and node attribute information, particularly when network observations are incomplete. This work presents SERM, a masked self-supervised framework for network-level structural representation learning. SERM integrates topology-aware graph propagation with masked self-supervised reconstruction. Node-level structural attributes are propagated according to the normalized network topology, enabling attribute information and multi-hop neighborhood context to interact directly within the encoder. Masked reconstruction then provides the self-supervised learning objective by requiring the model to recover hidden node attributes from the available attributes and graph context. During training, a subset of node attributes is masked and reconstructed from the available attributes and graph context, encouraging the encoder to exploit information from both sources without requiring external labels. The resulting node representations are aggregated into fixed-dimensional network-level embeddings for downstream analysis. Experiments on complex-network datasets evaluate the learned representations through network retrieval, structural property prediction, cross-dataset evaluation, robustness analysis, and ablation studies. The results provide empirical evidence that the proposed framework captures useful structural information and remains applicable across several network-level evaluation settings.