Dynamics of social balance on networks: The emergence of multipolar societies,Physical Review E

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Dynamics of social balance on networks: The emergence of multipolar societies
Physical Review E ( IF 2.2 ) Pub Date : 2021-09-09 , DOI: 10.1103/physreve.104.034303
Pouya Manshour _{1,

2} , Afshin Montakhab ₃

Affiliation

Within the context of social balance theory, much attention has been paid to the attainment and stability of unipolar or bipolar societies. However, multipolar societies are commonplace in the real world, despite the fact that the mechanism of their emergence is much less explored. Here, we investigate the evolution of a society of interacting agents with friendly (positive) and enmity (negative) relations into a final stable multipolar state. Triads are assigned energy according to the degree of tension they impose on the network. Agents update their connections to decrease the total energy (tension) of the system, on average. Our approach is to consider a variable energy

ε \in [0, 1]

for triads which are entirely made of negative relations. We show that the final state of the system depends on the initial density of the friendly links

ρ_{0}

. For initial densities greater than an

ε

-dependent threshold

ρ_{0}^{c} (ε)

, a unipolar (paradise) state is reached. However, for

ρ_{0} \leq ρ_{0}^{c} (ε)

, multipolar and bipolar states can emerge. We observe that the number of stable final poles increases with decreasing

ε

where the first transition from bipolar to multipolar society occurs at

ε^{*} \approx 0.67

. We end the paper by providing a mean-field calculation that provides an estimate for the critical (

ε

dependent) initial positive link density, which is consistent with our simulations.

中文翻译：

网络上的社会平衡动态：多极社会的出现

在社会平衡理论的背景下，单极或双极社会的实现和稳定受到了很多关注。然而，多极社会在现实世界中是司空见惯的，尽管其出现的机制很少被探索。在这里，我们调查了一个由具有友好（积极）和敌对（消极）关系的交互代理组成的社会演变为最终稳定的多极状态。三合会根据它们对网络施加的张力程度来分配能量。代理更新它们的连接以平均降低系统的总能量（张力）。我们的方法是考虑一个可变能量