Cross-frequency interactions during diffusion on complex networks are facilitated by scale-free properties

We studied the interactions between different temporal scales of diffusion processes on complex networks and found them to be stronger in scale-free (SF) than in Erdos-Renyi (ER) networks, especially for the case of phase-amplitude coupling (PAC)-the phenomenon where the phase of an oscillatory mode modulates the amplitude of another oscillation. We found that SF networks facilitate PAC between slow and fast frequency components of the diffusion process, whereas ER networks enable PAC between slow-frequency components. Nodes contributing the most to the generation of PAC in SF networks were non-hubs that connected with high probability to hubs. Additionally, brain networks from healthy controls (HC) and Alzheimer's disease (AD) patients presented a weaker PAC between slow and fast frequencies than SF, but higher than ER. We found that PAC decreased in AD compared to HC and was more strongly correlated to the scores of two different cognitive tests than what the strength of functional connectivity was, suggesting a link between cognitive impairment and multi-scale information flow in the brain.