Functional brain networks derived from resting-state functional magnetic resonance imaging (rs-fMRI) are commonly analyzed using graph-theoretical approaches, where correlation matrices are thresholded to form adjacency matrices. However, the choice of threshold is often arbitrary, leading to variability in network metrics and challenges in reproducibility. Here, we introduce a spectral method to identify a data-driven critical threshold in functional connectivity networks, defined by the point of maximal curvature in the algebraic connectivity (λ₂, the second-smallest eigenvalue of the graph Laplacian) as a function of the absolute correlation threshold. This critical threshold corresponds to an instability regime where the network begins to fragment, and the associated λ₂ value—termed λ₂* (lambda2ₛtar) —serves as a marker of network robustness. Using the Autism Brain Imaging Data Exchange (ABIDE) dataset (n = 931 subjects), we computed λ₂* for each subject's functional network based on the Automated Anatomical Labeling (AAL) atlas (116 regions of interest, ROIs). The distribution of λ₂* is approximately normal with a mean of 7. 43 (SD = 2. 21), ranging from 1. 16 to 15. 53. We observed site-specific variations in λ₂*, reflecting potential differences in data acquisition protocols across the 17 ABIDE sites. Furthermore, exploratory group comparisons revealed higher rates of network disconnection at the critical threshold in autism spectrum disorder (ASD) subjects (56%) compared to typically developing controls (CTRL; 30%), yielding an odds ratio of 3. 05, suggesting reduced network robustness in ASD. This method provides a reproducible, threshold-independent metric for characterizing functional brain networks, with applications in network neuroscience, biomarker discovery, and methodological standardization. The full pipeline is implemented in Python and is openly available, ensuring complete reproducibility from publicly accessible ABIDE ROI time series.
Janos Gabor Melegh (Tue,) studied this question.