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To reveal the coupling mechanism between structure and function in complex systems， a class of multilayer weighted edge corona network models is constructed， and their Laplacian spectral properties as well as first-order and second-order coherence behaviors are systematically analyzed， aiming to provide a theoretical basis for the robust design of multi-agent systems. Firstly， based on graph theory and matrix analysis， the Laplacian spectrum of the multilayer weighted edge corona network is derived using Kronecker product operations and block matrix eigenvalue decomposition. Then， exact expressions for first-order and second-order coherence are obtained from the Laplacian spectrum， and the influences of the number of layers， weights， and factor network topologies on coherence behavior and robustness are examined. As an application， the number of spanning trees and the Laplacian energy of the network are further computed. The results show that second-order coherence is more sensitive to topological changes than first-order coherence， and increasing the number of layers and weights can significantly enhance network robustness. For the same G2， when the factor network G1 possesses higher network coherence， the multilayer weighted edge corona network ■ generally exhibits higher first-order coherence and lower second-order coherence. For the same G1， when the factor network G2 possesses higher network coherence， the multilayer weighted edge corona network ■ also generally exhibits higher network coherence. These findings clarify the intrinsic coupling law between topology and coherence in multilayer weighted edge corona networks， providing a theoretical foundation for flexibly regulating the cooperative ability and anti-interference performance of multi-agent systems by adjusting the number of layers and weights.
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Basic Information:
China Classification Code:O157.5
Citation Information:
[1]LIU Jiabao,LI Qichang.Laplacian spectra and coherence of a class of multilayer weighted edge corona networks[J].Journal of Nantong University (Natural Science Edition)().
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安徽省自然科学基金项目（2508085MA017）
2026-06-26
2026-06-26
2026-06-26