Diffusion on Complex Networks : A way to probe their large scale topological structures

TL;DR

This paper introduces a diffusion-based method to analyze large-scale topological structures of complex networks, successfully revealing known and unknown modular features in real-world networks like social and Internet routing networks.

Contribution

It presents a novel diffusion approach focusing on slowest decaying modes to uncover and quantify the modular structure of complex networks.

Findings

Successfully identified known modules in a friendship network.

Revealed modular structure in the Internet network associated with countries.

Found that the Internet's slowest modes have a participation ratio about 10 times larger than a random network.

Abstract

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 finds 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.