Diverse phase transitions in optimized directed network models with distinct inward and outward node weights.
Rong-Chih Chang1, An-Liang Cheng1, Pik-Yin Lai1,2
1Department of Physics and Center for Complex Systems, National Central University, Chung-Li District, Taoyuan City 320, Taiwan, Republic of China.
Physical Review. E
|April 19, 2023
Summary
This study models directed network growth to minimize connection costs while optimizing network properties. Researchers used statistical mechanics and an Ising spin model to analyze phase transitions, including novel behaviors with negative node weights.
Area of Science:
- Statistical physics
- Network science
- Complex systems
Background:
- Directed network models are crucial for understanding complex systems.
- Optimizing network properties like connection costs and node degrees is a key challenge.
- Previous models often overlooked negative node weights and diverse phase transition behaviors.
Purpose of the Study:
- To develop and analyze directed network growth models.
- To investigate network properties under cost minimization and objective function optimization.
- To explore phase transitions, including those influenced by negative node weights.
Main Methods:
- Employed statistical mechanics methods.
- Mapped the directed network growth to an Ising spin model.
- Extended zero-temperature simulation algorithms for directed networks and negative weights.
Main Results:
- Derived analytic results for network growth models with general edge and node weight distributions.
- Identified diverse phase transition behaviors, including first-order, second-order, and hybrid transitions.
- Characterized novel phase transitions in the presence of negative node weights, including reentrance and symmetry-induced transitions.
- Developed efficient algorithms to obtain minimal cost configurations.
Conclusions:
- The study provides a comprehensive framework for understanding directed network growth.
- The findings reveal rich phase transition dynamics, particularly with negative node weights.
- The developed methods offer efficient solutions for optimizing network configurations.
- The results have implications for various applications in network science and beyond.
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