Healthy brain dynamics exhibit high flexibility and a wide range of spatiotemporal activity patterns, essential for adaptability and dynamic reorganization. Reduced flexibility and a narrower range of activity configurations are linked to neurological disease. Theoretical and experimental results support the hypothesis that a healthy brain operates in a critical regime, at the edge of a phase transition, where spontaneous activity is composed of scale-free avalanches of activity, and it enhances computational efficiency and responsiveness to stimuli. In this work, we investigate the spectra of eigenvalues of the similarity matrix between avalanche configurations, derived from analyzing avalanche activity in magnetoencephalography source-reconstructed signals and in a modular spiking neural model. By examining the distribution of eigenvalues and the reordered eigenvalue spectra ( \(\lambda \) vs. rank/N), we identify distinct behavior in the subcritical and critical regimes of the model. By comparing the experimental data with synthetic model results, we find similar behaviour when the model is tuned to a critical regime. This demonstrates that studying scalar invariants can identify matrices with structures close to those observed empirically.