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.
Du et al. (Sun,) studied this question.