Structure and dynamics analysis of brain functional hypernetworks based on the null models

Brain functional hypernetworks that can characterize the complex and multivariate interactions among multiple brain regions have been widely used in the diagnosis and prediction of brain diseases. However, there are few studies on the structure and dynamics of brain functional hypernetworks. Such studies can help to explore how the important functional features of brain functional hypernetworks characterize the working and pathological mechanisms of the human brain. Therefore, this article introduces the hypernetwork null model to analyze the dependencies between the features of interest. Specifically, first, based on the original brain functional hypernetwork, this article proposed the optimized hyper dK-series algorithm with hyperedges to construct null models that preserved the different node attributes and hyperedge attributes of the original brain functional hypernetwork, respectively. Next, based on the original hypernetwork model and the null model, multiple node attributes and hyperedge attributes were respectively introduced. Then, the level of similarity and correlation between the topological attributes of the original brain functional hypernetwork and the topological attributes of the brain functional hypernetwork null model were calculated to analyze the dependencies between the features of interest. The results showed that there were differences in the level of dependence between the features of interest. Node degree is the main dependency attribute for multiple metrics. Hyperedge degree, node degree-dependent redundancy coefficient, and hyperedge degree-dependent redundancy coefficient are partial dependency attributes for some metrics. The dependency attributes and level of dependency are the same for the hypernetwork clustering coefficients-HCC² and HCC³. This indicates that the node degree is redundant with respect to other attributes, while the hyperedge degree, node degree-dependent redundancy coefficient, and hyperedge degree-dependent redundancy coefficient perhaps contain other topology information. In addition, there is redundancy between HCC² and HCC³. Therefore, the effects of these redundant attributes need to be considered when performing network analysis.