Abrupt efficiency collapse in real-world complex weighted networks: robustness decrease with link weights heterogeneity

TL;DR

This study reveals that real-world complex weighted networks experience an abrupt efficiency collapse with minimal node or link removal, especially when link weights are highly heterogeneous, highlighting a vulnerability not captured by traditional connectivity measures.

Contribution

It demonstrates that network robustness assessments focusing solely on connectivity can significantly overestimate actual resilience, emphasizing the importance of weighted measures.

Findings

Abrupt efficiency collapse triggered by small node/link removal.

Weighted measures show vulnerability not detected by binary connectivity.

Heterogeneous link weights accelerate efficiency loss.

Abstract

Here we report a comprehensive analysis of the robustness of five high-quality real-world complex weighted networks to errors and attacks of nodes and links. We analyze C. Elegans, Cargo ship, E. Coli, Us Airports and Human brain real-world complex weighted networks. We use measures of the network damage conceived for a binary (e.g. largest connected cluster LCC, and binary efficiency Effbin) or a weighted network structure (e.g. the efficiency Eff, and the total energy-information En). We find that removing a very small fraction of nodes and links with respectively higher strength and weight triggers an abrupt collapse of the weighted functioning measures while measures that evaluate the binary-topological connectedness are almost unaffected. These findings unveil a problematic response-state of the real-world complex networks where the attack of a small fraction of nodes-links returns these systems in a connected but highly inefficient state. Our findings unveil how the robustness may be heavily overestimated focusing on the connectedness of the components only. Last, to understand how the networks robustness is generally affected by link weights heterogeneity, we randomly assign link weights over the topological structure of the real-world networks. We find that highly heterogeneous networks experienced a faster efficiency decrease under nodes-links removal: i.e. the robustness of the real-world complex networks against both random than attack is negatively correlated with links weight heterogeneity.