  We study the spectral properties of a diffusion process taking place on the
Internet network focusing on the slowest decaying modes. These modes allow us
to identify an underlying modular structure of the Internet roughly
corresponding to individual countries. For instance in the slowest decaying
mode the diffusion current flows from Russia towards US military sites. These
two regions thus constitute the extreme edges of the Internet. Quantitatively
the modular structure of the Internet manifests itself in approximately 10
times larger participation ratio of its slow decaying modes compared to the
null model - 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 we
measured this fraction to be around 30%. Finally we suggest, that the degree of
isolation of an individual module can be assessed by comparing its
participation in different diffusion modes. Using the proportionality of
response as a criterion we find that the independent module approximation works
well for the Internet.
