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Here we report a comprehensive analysis of the robustness of fivehigh-quality real-world complex weighted networks to errors and attacks ofnodes and links. We analyze C. Elegans, Cargo ship, E. Coli, Us Airports andHuman brain real-world complex weighted networks. We use measures of thenetwork damage conceived for a binary (e.g. largest connected cluster LCC, andbinary efficiency Effbin) or a weighted network structure (e.g. the efficiencyEff, and the total energy-information En). We find that removing a very smallfraction of nodes and links with respectively higher strength and weighttriggers an abrupt collapse of the weighted functioning measures while measuresthat evaluate the binary-topological connectedness are almost unaffected. Thesefindings unveil a problematic response-state of the real-world complex networkswhere the attack of a small fraction of nodes-links returns these systems in aconnected but highly inefficient state. Our findings unveil how the robustnessmay be heavily overestimated focusing on the connectedness of the componentsonly. Last, to understand how the networks robustness is generally affected bylink weights heterogeneity, we randomly assign link weights over thetopological structure of the real-world networks. We find that highlyheterogeneous networks experienced a faster efficiency decrease undernodes-links removal: i.e. the robustness of the real-world complex networksagainst both random than attack is negatively correlated with links weightheterogeneity.

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