Abstract: Traditional entropy method can effectively quantify the nonlinear characteristics of mechanical fault vibration signals, but its ability to represent the overall complexity of complex structures is limited, and structural evolution characteristics at different scales are difficult to capture. To address these challenges, a graph-domain complexity measurement method termed two-dimensional multi-scale graph Laplacian spectral entropy (MGLSE_2D) was proposed. First, a local energy-modulated visibility graph was constructed, in which geometric visibility relationship is modulated by node neighborhood energy, and the edge weight is exponentially enhanced. Second, a spectral probability model was established based on the eigenvalue distribution of the graph Laplacian matrix, and node connectivity and global topological information are introduced into the complexity measurement. Then, a two-dimensional multi-scale coarse-graining mechanism was employed to characterize the global structural complexity of vibration signals in the spectral domain across multiple scales. Furthermore, a hierarchical differential hippopotamus algorithm optimized support vector machine (HDHO-SVM) was employed for pattern recognition, and parameter optimization performance is improved through hierarchical search and differential perturbation mechanism. After that, a fault diagnosis method of rolling bearing based on MGLSE_2D and HDHO-SVM was constructed. Finally, simulation experiments and measured bearing data were used to validate the proposed method. The results demonstrate that the proposed diagnosis method achieves a classification accuracy of 99.11% and outperforms five comparative methods, exhibiting superior feature characterization ability and fault diagnosis performance.