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Heider and coevolutionary balance: From discrete to continuous phase transition
A Kargaran1, G R Jafari1,2
1Department of Physics, Shahid Beheshti University, G.C., Evin, Tehran 19839, Iran.
Physical Review. E
|June 17, 2021
Summary
This study compares two models of social network balance. Coevolutionary balance shows a continuous phase transition, unlike the discrete transition seen in Heider balance, with critical temperature dependent on network size.
Area of Science:
- Social network analysis
- Statistical mechanics
- Complex systems
Background:
- Structural balance in social networks is crucial for understanding group dynamics.
- Two primary models exist: Heider balance (link dynamics) and coevolutionary balance (node and link dynamics).
- Temperature, representing average irrationality, influences network stability.
Purpose of the Study:
- To investigate how temperature affects structural balance in social complex networks.
- To differentiate the phase transition behaviors of Heider balance and coevolutionary balance models.
- To analyze the relationship between critical temperature and network size for both models.
Main Methods:
- Utilizing statistical mechanics principles.
- Employing analytical calculations.
- Conducting numerical simulations on network models.
Main Results:
- Heider balance exhibits a discrete phase transition with temperature.
- Coevolutionary balance demonstrates a continuous phase transition.
- Critical temperature scales with the square root of network size in the coevolutionary model.
Conclusions:
- Coevolutionary balance offers a distinct dynamic compared to Heider balance under varying irrationality.
- The network size linearly influences the critical temperature in thermal Heider balance.
- Understanding these distinct transition behaviors is key to modeling social network stability.