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Navigability of complex networks

Nature Physics volume 5, pages 74–80 (2009)Cite this article

Abstract

Routing information through networks is a universal phenomenon in both natural and man-made complex systems. When each node has full knowledge of the global network connectivity, finding short communication paths is merely a matter of distributed computation. However, in many real networks, nodes communicate efficiently even without such global intelligence. Here, we show that the peculiar structural characteristics of many complex networks support efficient communication without global knowledge. We also describe a general mechanism that explains this connection between network structure and function. This mechanism relies on the presence of a metric space hidden behind an observable network. Our findings suggest that real networks in nature have underlying metric spaces that remain undiscovered. Their discovery should have practical applications in a wide range of areas where networks are used to model complex systems.

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Figure 1: How hidden metric spaces influence the structure and function of complex networks.
Figure 2: Average length of greedy-routing paths.
Figure 3: Success probability of greedy routing.
Figure 4: Greedy routing in the airport network.
Figure 5: Probability that greedy routing travels to higher-degree nodes.
Figure 6: The structure of greedy-routing paths.

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Acknowledgements

We thank M. Á. Serrano for useful comments and discussions. This work was supported in part by DGES grant FIS2007-66485-C02-02, Generalitat de Catalunya grant No. SGR00889, the Ramón y Cajal program of the Spanish Ministry of Science, by NSF CNS-0434996 and CNS-0722070, by DHS N66001-08-C-2029 and by Cisco Systems.

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Authors and Affiliations

  1. Departament de Física Fonamental, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain

    Marián Boguñá

  2. Cooperative Association for Internet Data Analysis (CAIDA), University of California, San Diego (UCSD), 9500 Gilman Drive, La Jolla, California 92093, USA

    Dmitri Krioukov & K. C. Claffy

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  1. Marián Boguñá
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  3. K. C. Claffy
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Correspondence to Marián Boguñá.

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Boguñá, M., Krioukov, D. & Claffy, K. Navigability of complex networks. Nature Phys 5, 74–80 (2009). https://doi.org/10.1038/nphys1130

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