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Hierarchical organization in complex networks.
Erzsébet Ravasz1, Albert-László Barabási
1Department of Physics, 225 Nieuwland Science Hall, University of Notre Dame, Notre Dame, IN 46556, USA.
Summary
Complex networks in nature and society exhibit scale-free and high clustering properties due to hierarchical organization. This structure follows a strict scaling law, identifiable in real-world networks like the World Wide Web.
Area of Science:
- Network Science
- Complex Systems Analysis
- Statistical Physics
Background:
- Real-world networks often exhibit scale-free topology and high clustering.
- These properties are fundamental to understanding the structure and function of complex systems.
Purpose of the Study:
- To investigate the underlying organizational principle responsible for scale-free topology and high clustering in real networks.
- To identify a quantifiable characteristic of hierarchical organization in complex systems.
Main Methods:
- Analysis of network properties, specifically degree distribution and clustering coefficients.
- Development and application of a scaling law to identify hierarchical organization.
- Examination of various real-world networks including the World Wide Web, actor networks, and the Internet.
Main Results:
- Scale-free topology and high clustering are direct consequences of hierarchical organization.
- A strict scaling law governs the degree of clustering within different groups in hierarchical networks.
- Several real-world networks, including the World Wide Web and the Internet, adhere to this identified scaling law.
Conclusions:
- Hierarchical organization is a fundamental characteristic of many complex systems.
- The discovered scaling law provides a method for detecting hierarchical structures in real networks.
- Understanding network hierarchy is crucial for comprehending the behavior of natural and social systems.