A lightweight deep learning-based model for ranking influential nodes in complex networks

Identifying influential nodes in complex networks is a critical task with a wide range of applications across different domains. However, existing approaches often face trade-offs between accuracy and computational efficiency. To address these challenges, we propose 1D-CGS, a lightweight hybrid model that integrates the speed of one-dimensional convolutional neural networks (1D-CNN) with the topological representation power of GraphSAGE for efficient node ranking. The model employs a lightweight input representation based on two straightforward and significant topological features: node degree and average neighbor degree. These features are processed through 1D convolutions to extract local patterns, followed by GraphSAGE layers to aggregate neighborhood information. We formulate node ranking as a regression problem and use the Susceptible–Infected–Recovered (SIR) model to generate ground truth influence scores. 1D-CGS is initially trained on synthetic Barabási–Albert networks and then applied to real-world networks. Experimental evaluations on twelve real-world networks demonstrate that 1D-CGS significantly outperforms traditional centrality methods and recent deep learning models in ranking accuracy, while maintaining very fast runtime. On these networks, the proposed model achieves average improvements of 4.73% and 7.67% over the best-performing deep learning baselines. It also achieves an average Monotonicity Index (MI) score of 0.9955, indicating highly unique and discriminative rankings. Furthermore, additional comparisons on benchmark networks show that 1D-CGS achieves the highest average Kendall’s Tau of 0.8165 among the evaluated approaches, confirming its strong generalization capability. Overall, the results demonstrate that 1D-CGS is both efficient and scalable, making it suitable for large-scale applications.