Multiscale Node-Edge Interactions in Complex Networks: A Case Study Using Brain Network

In complex networks, researching the relationships between nodes and edges has been a hot topic in recent years. However, to date, no studies have explored the multiscale node-edge interaction (MNEI) information within complex networks.

As an illustrative example, the study employs brain networks of individuals diagnosed with Alzheimer's disease, mild cognitive impairment, and healthy controls. Our approach begins by decomposing the node and edge attributes from the vertex domain into nine MNEI components within the graph frequency domain. Each component encapsulates joint information, integrating either high, middle, or low graph frequency bands for node attributes, along with any band from the edge attributes. Following this, we transform each MNEI component back into the vertex domain to enable further analysis. Ultimately, the MNEI features derived from both domains are employed to classify subjects into three distinct groups.

A majority of MNEI features display significant differences among the groups, resulting in classification performance that surpasses traditional brain network analysis methods.

Importantly, this study is the first to demonstrate the capability of capturing MNEI in complex networks. Additionally, this research can be regarded as a novel information fusion technique for integrating node and edge attributes under non-Euclidean network topological constraints. Furthermore, this approach can also be considered a new type of multi-scale complex network decomposition.

Overall, these advancements have expanded the scope of complex network analysis and provided brand-new scientific insights, with the potential for widespread application in numerous fields in the future.