Efficiency and robustness of eigenvector methods for cluster detection in weighted networks

Abstract In this work, we compare two eigenvector-based approaches for detecting clusters in complex weighted networks: the Laplacian spectral localization method and the eigenvector centrality method. We apply both techniques to two representative networks and evaluate their outputs against synchronization dynamics to measure detection accuracy. We show that the Laplacian spectral localization method not only identifies cluster compositions but also predicts the sequence of cluster formation, providing deeper insight into the synchronization process. To structure the comparison, we proceed in two stages. First, we evaluate the structural accuracy of the detected clusters in the absence of noise and compare the results with the synchronization error, factor diagrams, and Hamiltonian energy. Second, we introduce slight noise into the adjacency matrix to test the robustness of each method under identical tolerance thresholds. Our results demonstrate that the Laplacian spectral localization method is able to capture intermediate synchronization patterns that the eigenvector centrality method misses and maintains reliable accuracy at higher noise intensities. These findings offer practical guidance for selecting suitable cluster detection techniques in both ideal and noisy network environments.