Dangling centrality highlights critical nodes by evaluating network stability through link removal.

This study introduces "Dangling Centrality," a novel metric for identifying critical nodes in networks by assessing the impact of their link removal on system dynamics. The proposed metric is validated on real-world datasets, including Amazon product networks, a Protein-Protein Interaction (PPI) network, and a Bitcoin network, offering insights into key products, critical proteins, and influential entities. These nodes, as the main pillars of system propagation, are crucial for maintaining the structural and functional integrity of the network. By removing the links of these nodes, the network's stability, flow, and communication can be disrupted, highlighting their importance. Additionally, small-scale 5-node and 6-node networks are analyzed to demonstrate the metric's behavior in simpler contexts. Correlation analyses using Pearson's, Spearman's, and Kendall's coefficients demonstrate alignment with traditional centrality metrics while providing a unique perspective. The findings emphasize the metric's practical utility in understanding network vulnerabilities, enhancing resilience, and informing system design. Materials and implementations are available at: https://github.com/Ubaidafatima/Centrality-Measures .