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Hybrid balance theory: Heider balance under higher-order interactions
M H Hakimi Siboni1, A Kargaran1, G R Jafari1,2
1Department of Physics, Shahid Beheshti University, Evin, Tehran 1983969411, Iran.
Physical Review. E
|June 16, 2022
Summary
This study introduces a hybrid balance theory combining third- and fourth-order interactions in signed networks. Results show a threshold where higher-order interactions dominate, influencing network balance and allowing imbalances to persist.
Area of Science:
- Social network analysis
- Statistical physics
- Complex systems
Background:
- Heider's balance theory models relationships in signed networks, assuming independence of triadic relations.
- Real-world networks exhibit higher-order interactions beyond simple triadic relationships.
- Quartic balance considers the influence of neighboring triangles, challenging the independence assumption.
Purpose of the Study:
- To investigate how quartic balance (fourth-order interactions) affects Heider balance (third-order interactions).
- To develop and analyze a hybrid balance theory incorporating both third- and fourth-order interactions.
Main Methods:
- Developed a theoretical model integrating third- and fourth-order interactions.
- Employed mean-field approximation to analyze the model's phase diagram.
- Validated findings using Monte Carlo simulations.
Main Results:
- Identified a critical threshold for higher-order interaction strength.
- Below the threshold, third-order interactions dominate, leading to balanced networks.
- Above the threshold, fourth-order interactions become significant, allowing for the survival of imbalanced triangles.
- Observed a first-order phase transition related to agent behavior (temperature).
Conclusions:
- Hybrid balance theory explains the interplay between third- and fourth-order interactions in signed networks.
- Network balance is critically dependent on the strength of higher-order interactions.
- The findings align with simulations, suggesting a robust phase transition phenomenon.
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