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Error and attack tolerance of complex networks

A Corrigendum to this article was published on 25 January 2001

Abstract

Many complex systems display a surprising degree of tolerance against errors. For example, relatively simple organisms grow, persist and reproduce despite drastic pharmaceutical or environmental interventions, an error tolerance attributed to the robustness of the underlying metabolic network1. Complex communication networks2 display a surprising degree of robustness: although key components regularly malfunction, local failures rarely lead to the loss of the global information-carrying ability of the network. The stability of these and other complex systems is often attributed to the redundant wiring of the functional web defined by the systems' components. Here we demonstrate that error tolerance is not shared by all redundant systems: it is displayed only by a class of inhomogeneously wired networks, called scale-free networks, which include the World-Wide Web3,4,5, the Internet6, social networks7 and cells8. We find that such networks display an unexpected degree of robustness, the ability of their nodes to communicate being unaffected even by unrealistically high failure rates. However, error tolerance comes at a high price in that these networks are extremely vulnerable to attacks (that is, to the selection and removal of a few nodes that play a vital role in maintaining the network's connectivity). Such error tolerance and attack vulnerability are generic properties of communication networks.

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Figure 1: Visual illustration of the difference between an exponential and a scale-free network.
Figure 2: Changes in the diameter d of the network as a function of the fraction f of the removed nodes.
Figure 3: Network fragmentation under random failures and attacks.
Figure 4: Summary of the response of a network to failures or attacks.

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Acknowledgements

We thank B. Bunker, K. Newman, Z. N. Oltvai and P. Schiffer for discussions. This work was supported by the NSF.

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Correspondence to Albert-László Barabási.

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Albert, R., Jeong, H. & Barabási, AL. Error and attack tolerance of complex networks. Nature 406, 378–382 (2000). https://doi.org/10.1038/35019019

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