Multi-Indicator Entropy Hub Score: A quantitative approach to hub analysis in brain networks

The human brain depends on dynamic interactions among modular networks, where connector and provincial hubs facilitate efficient information integration. Most previous studies have relied on single metrics or qualitative labels to identify hubs, overlooking multi-metric integration and the quantitative contributions of nodes. Here, we introduce the Multi-Indicator Entropy Hub Score (MIEHS), which integrates six graph-theoretical metrics to quantify hub properties. Validated on benchmark and simulated networks as well as resting-state fMRI data from the Midnight Scan Club dataset, MIEHS reliably identifies hubs. High-scoring connector hubs were localized in the attention network, whereas high-scoring provincial hubs were concentrated in the default mode network. Gradient mapping further revealed that connector hubs bridge unimodal and transmodal regions, supporting information transfer from primary sensory areas to higher-order cognitive regions, while provincial hubs primarily sustain intra-network communication. Null model analyses highlighted the stability of hubs within the default mode and limbic networks. Although hubs are widely studied, they have not yet been established as robust clinical biomarkers. Using Partial Least Squares analysis in the UCLA dataset (HC = 110, ADHD = 37, BD = 40, SCHZ = 37), we observed significant associations between hub alterations in the DMN, SMN, limbic, DAN, and control networks and measures of cognitive flexibility, abstract reasoning, and verbal expression. Together, these findings demonstrate that MIEHS provides a robust and versatile framework for mapping brain network organization and characterizing functional reconfiguration.