Ingve Simonsen, Kasper Astrup Eriksen, Sergei Maslov,
and Kim Sneppen
Diffusion on complex networks: a way to probe their
large-scale topological structures
Physica A 336, 163-173 (2004)
A diffusion process on complex networks is introduced in
order to uncover their large-scale topological structures.
This is achieved by focusing on the slowest decaying
diffusive modes of the network. The proposed procedure is
applied to real-world networks like a friendship network of
known modular structure, and an Internet routing network.
For the friendship network, its known structure is well
reproduced. In case of the Internet, where the structure is
far less well known, one indeed 5nds a modular structure,
and modules can roughly be associated with individual
countries. Quantitatively, the modular structure of the
Internet manifests itself in an approximately 10 times
larger participation ratio of its slowest decaying modes as
compared to the null model a random scale-free network. The
extreme edges of the Internet are found to correspond to
Russian and US military sites.
LU TP 04-17