Predicting Dependent Edges in Nonequilibrium Complex Systems Based on Overlapping Module Characteristics

Problem: Predicting dependency relationships in nonequilibrium systems is a critical challenge in complex systems research. Solution proposed: In this paper, we propose a novel method for predicting dependent edges in network models of nonequilibrium complex systems, based on overlapping module features. This approach addresses the many-to-many dependency prediction problem between nonequilibrium complex networks. By transforming node-based network models into edge-based models, we identify overlapping modular structures, enabling the prediction of many-to-many dependent edges. Experimental evaluation: This method is applied to dependency edge prediction in power and gas networks, curriculum and competency networks, and text and question networks. Results: The results indicate that the proposed dependency edge prediction method enhances the robustness of the network in power–gas networks, accurately identifies supporting relationships in curriculum–competency networks, and achieves better information gain in text–question networks. Conclusion: These findings confirm that the overlapping module-based approach effectively predicts dependencies across various nonequilibrium complex systems in diverse fields.