Modularity and Extreme Edges of the Internet

摘要

We study the spectral properties of a diffusion process taking place on theInternet network focusing on the slowest decaying modes. These modes allow usto identify an underlying modular structure of the Internet roughlycorresponding to individual countries. For instance in the slowest decayingmode the diffusion current flows from Russia towards US military sites. Thesetwo regions thus constitute the extreme edges of the Internet. Quantitativelythe modular structure of the Internet manifests itself in approximately 10times larger participation ratio of its slow decaying modes compared to thenull model - a random scale-free network. We propose to use the fraction ofnodes participating in slow decaying modes as a general measure of themodularity of a network. For the 100 slowest decaying modes of the Internet wemeasured this fraction to be around 30%. Finally we suggest, that the degree ofisolation of an individual module can be assessed by comparing itsparticipation in different diffusion modes. Using the proportionality ofresponse as a criterion we find that the independent module approximation workswell for the Internet.