Modularity and extreme edges of the internet

Area of Science:

• Network Science
• Complex Systems Analysis
• Information Diffusion Studies

Background:

• Understanding network structure is crucial for analyzing diffusion processes.
• The Internet exhibits complex modularity, influencing how information spreads.
• Previous studies often overlook the spectral properties of diffusion on large networks.

Purpose of the Study:

• To investigate the spectral properties of diffusion on the Internet network.
• To identify and characterize the slowest decaying modes of diffusion.
• To quantify the modular structure of the Internet using spectral analysis.

Main Methods:

• Analysis of spectral properties of a diffusion process on the Internet network.
• Focus on the slowest decaying modes to reveal underlying structures.
• Comparison with random scale-free network models.

Main Results:

• The slowest decaying diffusion modes highlight a modular structure, often corresponding to countries.
• The Internet's modularity is quantitatively demonstrated by a significantly larger participation ratio in slow modes compared to random networks.
• Approximately 30% of nodes participate in the 100 slowest decaying modes of the Internet.

Conclusions:

• The fraction of nodes in slow decaying modes serves as a robust measure of network modularity.
• Spectral analysis of diffusion modes can effectively assess the isolation of network modules.
• This approach provides insights into the global structure and information flow patterns of the Internet.