High-Order Interactions Reshape the Carbon Emission Efficiency Network Across Chinese Regions.

To address the challenge of balancing economic growth with carbon emission reduction, improving regional Carbon Emission Efficiency (CEE) has emerged as a central pathway to achieving the "dual carbon" goals. While most existing studies focus on inter-regional CEE linkages through pairwise interaction networks, such approaches fall short in capturing the high-order mechanisms of multi-regional collaboration. This study integrates the Super-SBM model with a modified gravity model to construct a CEE correlation network across 30 provincial administrative regions in China from 2007 to 2023. To overcome the limitations of traditional pairwise networks, simplicial complex theory is introduced to establish a high-order topological representation framework. Furthermore, by applying the multiorder Laplacian to assess the synchronization stability of the network, a directed second-order degree swap strategy is proposed to optimize its high-order structure. The findings reveal that the CEE correlation network has evolved from a single-pole aggregation pattern toward a multi-center equilibrium. Provinces with high connectivity play a dominant role in both pairwise and triadic synergies, though their collaborative advantages are gradually diffusing to central and western regions. Notably, with only a limited number (approximately five) of second-order degree swaps among key node pairs, the network's synchronization stability can be substantially improved. When first-order and second-order interaction strengths reach comparable levels (coupling strength α*≈0.5), the system achieves optimal resistance to external perturbations. This study highlights the pivotal role of high-order collaboration in shaping regional CEE linkages and offers a practical optimization pathway for structurally enhancing CEE through coordinated efforts in pursuit of the "dual carbon" goals.