Loops structure of the Internet at the autonomous system level

Area of Science:

• Network science
• Internet topology
• Graph theory

Background:

• The Internet's autonomous system (AS) level graph structure is dynamic.
• Understanding network evolution and stability is crucial for network management and design.

Purpose of the Study:

• To analyze the clustering and loop structures within the Internet's AS graph.
• To investigate the temporal stability of these structures and identify underlying network properties.

Main Methods:

• Analysis of AS-level Internet graph data.
• Statistical examination of loop distributions (order 3, 4, and 5).
• Investigation of two-point correlations between vertex degrees.

Main Results:

• Statistical distributions of loops of order 3, 4, and 5 remain stable over time.
• Internet graphs exhibit Markovian signatures, well-described by two-point degree correlations.
• The local and global structure of the Internet can be sufficiently characterized by these correlations.

Conclusions:

• Despite temporal changes, key structural properties like loop distributions are stable.
• The Internet's network topology is highly correlated, simplifying its structural description.
• Findings offer insights into network models and Internet evolution.