TY - JOUR
T1 - Modularity and Extreme Edges of the Internet
AU - Eriksen, Kasper Astrup
AU - Simonsen, Ingve
AU - Maslov, Sergei
AU - Sneppen, Kim
N1 - Funding Information:
The work at Brookhaven National Laboratory was carried out under Contract No. DE-AC02-98CH10886, Division of Material Science, U.S. Department of Energy. Two of us (K. E. and K. S.) thank the Institute for Strongly Correlated and Complex Systems at Brook?>haven National Laboratory for financial support during visits when part of this work was completed.
PY - 2003
Y1 - 2003
N2 - 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 [Formula presented]. Finally, we suggest that the degree of isolation of an individual module can be assessed by comparing its participation in different diffusion modes.
AB - 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 [Formula presented]. Finally, we suggest that the degree of isolation of an individual module can be assessed by comparing its participation in different diffusion modes.
UR - http://www.scopus.com/inward/record.url?scp=0037530428&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0037530428&partnerID=8YFLogxK
U2 - 10.1103/PhysRevLett.90.148701
DO - 10.1103/PhysRevLett.90.148701
M3 - Article
C2 - 12731952
AN - SCOPUS:0037530428
SN - 0031-9007
VL - 90
SP - 4
JO - Physical review letters
JF - Physical review letters
IS - 14
ER -