MIEHS: A Quantitative Approach to Hub Property Analysis in Brain Networks

The human brain relies on dynamic interactions among modular networks, where connector and provincial hubs critically enable information integration. However, existing hub characterization remains predominantly qualitative, overlooking the quantitative contributions of potential hub nodes. To address this gap, we introduce the Multi-Indicator Entropy Hub Score (MIEHS), a quantitative framework integrating six graph-theoretical metrics including betweenness/degree centrality, participation coefficient, within-module betweenness/degree centrality, and clustering coefficient, to holistically evaluate hub properties. We validated MIEHS using benchmark networks, random simulated networks, and resting-state fMRI data from the Midnight Scan Club dataset, demonstrating its accuracy and robustness in hub identification. Our findings reveal that high-score connector hubs predominantly localize within the attention network, while high-score provincial hubs are concentrated in the default mode network (DMN). Gradient mapping further indicates that connector hubs bridge unimodal and transmodal regions, facilitating the transition of information from primary sensory areas to higher-order cognitive regions, whereas provincial hubs primarily support intra-network communication. Additionally, random null model analysis highlights the stability of hub nodes within the DMN and limbic networks. Moreover, to explore clinical implications, we applied Partial Least Squares analysis to the UCLA dataset (HC=110, ADHD=37, BD=40, SCHZ=37), examining the relationship between hub properties and psychiatric symptoms. The results reveal significant associations between hub changes in DMN, SMN, limbic, DAN, and control networks with cognition and behavior. Notably, modifications in hub connectivity impact cognitive flexibility, abstract reasoning, and verbal expression. By bridging quantitative hub analysis with clinical phenotypes, MIEHS provides novel insights of brain network organization and demonstrated a robust tool for elucidating brain functional reconfiguration and functional organization. Keywords: brain networks, connector hubs, provincial hubs, resting-state fMRI, graph property analysis