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Phys Rev Lett. 2003 Apr 11;90(14):148701. Epub 2003 Apr 11.

Modularity and extreme edges of the internet.

Author information

1
The Nordic Institute for Theoretical Physics-NORDITA, Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark. kasper@nordita.dk

Abstract

We study the spectral properties of a diffusion process taking place on the Internet network focusing on the slowest decaying modes. These modes identify an underlying modular structure roughly corresponding to individual countries. For instance, in the slowest decaying mode the diffusion current flows from Russia to U.S. military sites. Quantitatively the modular structure manifests itself in a 10 times larger participation ratio of its slow decaying modes compared to a random scale-free network. We propose to use the fraction of nodes participating in slow decaying modes as a general measure of the modularity of a network. For the 100 slowest decaying modes of the Internet this fraction is approximately 30%. Finally, we suggest that the degree of isolation of an individual module can be assessed by comparing its participation in different diffusion modes.

PMID:
12731952
DOI:
10.1103/PhysRevLett.90.148701
[Indexed for MEDLINE]

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