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

## Details

**Authors** Ubaida Fatima, Saman Hina, Muhammad Wasif

**Year** 2025

**Publisher** Scientific Reports

**Kind of work** article

**Discipline** Network Science

**Secondary disciplines** Computer Science & AI

**Applied** false

[Read it at the publisher](https://doi.org/10.1038/s41598-025-24930-8) 
10.1038/s41598-025-24930-8

## In authors' words

### Abstract

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.

### What they set out to do (purpose)

To introduce and validate 'dangling centrality,' a metric for identifying critical nodes in networks by assessing how much removing a node's links destabilizes overall network communication.

### Who or what was studied (sample)

Two Amazon product co-purchase networks (up to roughly 403,000 nodes), a Bitcoin OTC trust network (5,881 nodes), a yeast protein-protein interaction network (2,361 nodes), and small 5- and 6-node test networks.

### How they did it (methods)

Computed shortest-path distance and adjacency matrices before and after removing a node's links, derived dangling centrality from the normalized change, and compared it to traditional centrality measures using Pearson, Spearman, and Kendall correlations.

### What they found (results)

Validated on Amazon product, Bitcoin, and protein-protein interaction networks, the proposed dangling-centrality metric identified critical nodes by measuring how much network-wide communication stability degrades when that node's links are removed, correlating with but offering distinct information from traditional centrality measures.

## Commentary

### In short

Demonstrates a system in which a part's relationships to the rest of the network determine the stability of the whole, operationalized by observing what happens when those links are removed.

**Patterns it shows** S, R

**Added** 2026-09-28

**How to cite this** Ubaida Fatima, Saman Hina, Muhammad Wasif (2025). Dangling centrality highlights critical nodes by evaluating network stability through link removal. Scientific Reports.