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Updated: Aug 6, 2026
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Published on: October 13, 2023
Statistical self-similar properties of complex networks
Chang-Yong Lee1, Sunghwan Jung
1The Department of Industrial Information, Kongju National University, Chungnam, 340-702 South Korea. clee@kongju.ac.kr
Summary
Complex networks exhibit multifractal properties in their clustering coefficient distribution, revealing universal statistical self-similarity. This finding offers a unified framework for understanding diverse complex network structures.
Area of Science:
- Network Science
- Statistical Physics
- Complex Systems Analysis
Background:
- Complex networks display unique features distinct from random or regular networks.
- Existing network characteristics are often network-type dependent, limiting universal applicability.
- A need exists to identify common, ubiquitous properties across diverse complex networks.
Purpose of the Study:
- To uncover universal characteristics shared by various complex networks.
- To analyze complex networks using statistical self-similarity.
- To employ the clustering coefficient as a probability measure for network analysis.
Main Methods:
- Statistical self-similarity analysis.
- Utilizing the clustering coefficient as a probability measure.
- Investigating diverse types of complex networks.
Main Results:
- The probability distribution of the clustering coefficient is characterized by multifractality.
- The support of the clustering coefficient measure exhibits a fractal dimension.
- These multifractal and fractal properties provide a unified description for complex networks.
Conclusions:
- Complex networks share ubiquitous characteristics describable by multifractality and fractal dimensions.
- The clustering coefficient's multifractal nature offers a unified approach to network analysis.
- This research opens new avenues for comprehending the fundamental properties of complex systems.
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