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Diffusion on complex networks: a way to probe their large-scale topological structures

Author

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  • Simonsen, Ingve
  • Astrup Eriksen, Kasper
  • Maslov, Sergei
  • Sneppen, Kim

Abstract

A diffusion process on complex networks is introduced in order to uncover their large-scale topological structures. This is achieved by focusing on the slowest decaying diffusive modes of the network. The proposed procedure is applied to real-world networks like a friendship network of known modular structure, and an Internet routing network. For the friendship network, its known structure is well reproduced. In case of the Internet, where the structure is far less well known, one indeed finds a modular structure, and modules can roughly be associated with individual countries. Quantitatively, the modular structure of the Internet manifests itself in an approximately 10 times larger participation ratio of its slowest decaying modes as compared to the null model—a random scale-free network. The extreme edges of the Internet are found to correspond to Russian and US military sites.

Suggested Citation

  • Simonsen, Ingve & Astrup Eriksen, Kasper & Maslov, Sergei & Sneppen, Kim, 2004. "Diffusion on complex networks: a way to probe their large-scale topological structures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(1), pages 163-173.
    • Handle: RePEc:eee:phsmap:v:336:y:2004:i:1:p:163-173
    DOI: 10.1016/j.physa.2004.01.021
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    Cited by:

    1. Park, Ji Hwan & Chang, Woojin & Song, Jae Wook, 2020. "Link prediction in the Granger causality network of the global currency market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).

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