Many researchers using many different approaches have attempted to find features discriminating between autism spectrum disorder (ASD) and typically control (TC) subjects. In this study, this attempt has been continued by analyzing global metrics of functional graphs and metrics of functional triadic interactions of the brain in the low, middle, and high-frequency bands (LFB, MFB, and HFB) of the structural graph. The graph signal processing (GSP) provided the combinatorial usage of the functional graph of resting-state fMRI and structural graph of DTI. In comparison to TCs, ASDs had significantly higher clustering coefficients in the MFB, higher efficiencies and strengths in the MFB and HFB, and lower small-world propensity in the HFB. These results show over-connectivity, more global integration, and probably decreased local specialization in ASDs compared to TCs. Triadic analysis showed that the numbers of unbalanced triads were significantly lower for ASDs in the MFB. This finding may show the reason for restricted and repetitive behavior in ASDs. Also, in the MFB and HFB, the numbers of balanced triads and the energies of triadic interactions were significantly higher and lower for ASDs, respectively. These findings may reflect the disruption of the optimum balance between functional integration and specialization. All of these results demonstrated that the significant differences between ASDs and TCs existed in the MFB and HFB of the structural graph when analyzing the global metrics of the functional graph and triadic interaction metrics. In conclusion, the results demonstrate the promising perspective of GSP for attaining discriminative features and new knowledge, especially in the case of ASD. Graphical Abstract
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