Unevenness of loop location in complex networks.

Area of Science:

• Network science
• Graph theory
• Complex systems analysis

Background:

• Loop structures are crucial in complex networks.
• Previous research indicates real networks have fewer loops than random models.
• The spatial distribution of loops in networks is not well understood.

Purpose of the Study:

• To investigate the uneven distribution of loops in complex networks.
• To identify network regions with high loop density ('rich loop cores').
• To develop a method for quantifying loop distribution unevenness.

Main Methods:

• A node removal process was employed to analyze loop distribution.
• The method was applied to real-world network datasets.
• A novel index was created to measure loop location unevenness.

Main Results:

• Uneven loop distribution is a common feature in complex networks.
• Rich loop cores were identified in networks like neural networks and food webs.
• The proposed index effectively quantifies this unevenness.

Conclusions:

• Complex networks display non-uniform loop arrangements.
• The findings highlight the importance of loop topology in network structure.
• The developed index offers a valuable tool for network analysis.