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Growing network with local rules: preferential attachment, clustering hierarchy, and degree correlations
1Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556, USA.
Summary
This study demonstrates that linear preferential attachment, crucial for understanding power-law networks, naturally emerges from local network growth rules. These local models also explain network clustering and degree correlations.
Area of Science:
- Complex Networks
- Network Science
- Statistical Physics
Background:
- The linear preferential attachment hypothesis successfully explains power-law degree distributions in networks.
- The origin of this mechanism as a consequence of general local rules remains an open question.
Purpose of the Study:
- To investigate if effective linear preferential attachment arises naturally from growing network models based on local rules.
- To explore if local models can explain other complex network properties like clustering hierarchy and degree correlations.
Main Methods:
- Development and analysis of growing network models governed by local rules.
- Employing both analytical and numerical approaches.
- Testing various local rules, including previously proposed models.
Main Results:
- Demonstrated that effective linear preferential attachment is an inherent outcome of network growth based on local rules.
- Showcased that these local models provide explanations for observed clustering hierarchy.
- Provided insights into the mechanisms behind degree correlations in complex networks.
Conclusions:
- Local rules in growing networks naturally lead to effective linear preferential attachment.
- Local models offer a unified explanation for key properties of complex networks, including degree distributions, clustering, and correlations.