To understand collective network behavior in the complex human brain, pairwise correlation networks alone are insufficient for capturing the high-order interactions that extend beyond pairwise interactions and play a crucial role in brain network dynamics. These interactions often reveal intricate relationships among multiple brain networks, significantly influencing cognitive processes. In this study, we explored the correlation of correlation networks and topological network analysis with resting-state fMRI to gain deeper insights into these higher-order interactions and their impact on the topology of brain networks, ultimately enhancing our understanding of brain function. We observed that the correlation of correlation networks highlighted network connections while preserving the topological structure of correlation networks. Our findings suggested that the correlation of correlation networks surpassed traditional correlation networks, showcasing considerable potential for applications in various areas of network science. Moreover, after applying topological network analysis to the correlation of correlation networks, we observed that some high-order interaction hubs predominantly occurred in primary and high-level cognitive areas, such as the visual and fronto-parietal regions. These high-order hubs played a crucial role in information integration within the human brain.

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