Renormalization of networks with weak geometric coupling

Area of Science:

• Complex systems analysis
• Network science
• Statistical physics

Background:

• The renormalization group is fundamental for studying systems across various scales.
• Network geometry, which bases topology on node locations in a hidden metric space, is a key renormalization approach.
• Existing methods often assume strong geometric coupling, overlooking weak coupling prevalent in real-world networks.

Purpose of the Study:

• To extend renormalization techniques to networks with weak geometric coupling.
• To investigate the role of geometric information in preserving network self-similarity under weak coupling conditions.

Main Methods:

• Development of a renormalization framework applicable to weak geometric coupling in networks.
• Analysis of network topology considering node positions in a hidden metric space.

Main Results:

• Demonstration that geometric information remains crucial for self-similarity even with weak coupling.
• Identification of the significance of geometric effects on network topology under weak coupling.

Conclusions:

• Network geometry plays a critical role in maintaining self-similarity, irrespective of coupling strength.
• The study highlights the importance of considering geometric influences on network topology, particularly in scenarios with weak coupling.