The Coupling Mechanism of the Electricity–Gas System and Assessment of Attack Resistance Based on Interdependent Networks

Natural gas plays a critical role in integrated energy systems. In this context, the present study proposes an optimization model for the electricity–gas coupling system, grounded in the theory of interdependent networks. By integrating network topology parameters with real-time operational metrics, the model substantially enhances system robustness and adaptability. To quantify nodal vulnerability and importance, the study introduces two novel evaluation indicators: the Electric Potential–Closeness Fusion Indicator (EPFI) for power networks and the Pressure Difference–Closeness Comprehensive Indicator (PDCI) for natural gas systems. Leveraging these indicators, three coupling paradigms—assortative, disassortative, and random—are systematically constructed and analyzed. System resilience is assessed through simulation experiments incorporating three attack strategies: degree-based, betweenness centrality-based, and random node removal. Evaluation metrics include network efficiency and the variation in the size of the largest connected subgraph under different coupling configurations. The proposed framework is validated using a hybrid case study that combines the IEEE 118-node electricity network with a 20-node Belgian natural gas system, operating under a unidirectional gas-to-electricity energy flow model. Results confirm that the disassortative coupling configuration, based on EPFI and PDCI indicators, exhibits superior resistance to network perturbations, thereby affirming the effectiveness of the model in improving the robustness of integrated energy systems.