Modularity and Extreme Edges of the Internet

The spectral properties of a diffusion process taking place on the Internet network have studied 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. The authors have proposed 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 ∼30%. Finally, they have suggested that the degree of isolation of an individual module can be assessed by comparing its participation in different diffusion modes.

Ref: K. A. Eriksen, I. Simonsen,  S. Maslov and  K. Sneppen;  Phys. Rev. Lett. 90, 148701 (2003)