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Nonlocal evolution of weighted scale-free networks.
1School of Physics and Center for Theoretical Physics, Seoul National University NS50, Seoul 151-747, Korea.
Summary
We introduce globally updating evolution for weighted networks, explaining nonlinear scaling between node strength and degree. This new model generalizes existing schemes to nonlinear preferential attachment, creating simultaneous power-law behaviors.
Area of Science:
- Network Science
- Complex Systems
- Data Communications
Background:
- Weighted networks are crucial for modeling data transport.
- Existing models often lack explanations for nonlinear scaling in network properties.
- Node strength and degree are key network metrics.
Purpose of the Study:
- Introduce a novel 'globally updating evolution' model for weighted networks.
- Explain the nonlocal determination of packet transport and its effect on network structure.
- Generalize existing strength-driven evolution schemes to nonlinear preferential attachment.
Main Methods:
- Developed a theoretical framework for globally updating evolution in weighted networks.
- Analyzed the nonlocal nature of data packet transport.
- Proposed and simulated a simple model demonstrating nonlinear preferential attachment.
Main Results:
- Established a method to explain generic nonlinear scaling between node strength and degree.
- Demonstrated simultaneous power-law behavior in both degree and strength.
- Showcased the generalization of strength-driven evolution to nonlinear preferential attachment.
Conclusions:
- The globally updating evolution model provides a unified explanation for network scaling properties.
- Nonlinear preferential attachment rules can generate complex network behaviors.
- This framework advances the understanding of dynamic weighted networks and data transport.