Faculty of Physics, Warsaw University of Technology, Koszykowa 75, PL 00-662 Warsaw, Poland.
ITMO University, Kronverkskiy avenue 49, RU 197101 Saint Petersburg, Russia.
Phys Rev Lett. 2020 Aug 14;125(7):078302. doi: 10.1103/PhysRevLett.125.078302.
Homophily between agents and structural balance in connected triads of agents are complementary mechanisms thought to shape social groups leading to, for instance, consensus or polarization. To capture both processes in a unified manner, we propose a model of pair and triadic interactions. We consider N fully connected agents, where each agent has G underlying attributes, and the similarity between agents in attribute space (i.e., homophily) is used to determine the link weight between them. For structural balance we use a triad-updating rule where only one attribute of one agent is changed intentionally in each update, but this also leads to accidental changes in link weights and even link polarities. The link weight dynamics in the limit of large G is described by a Fokker-Planck equation from which the conditions for a phase transition to a fully balanced state with all links positive can be obtained. This "paradise state" of global cooperation is, however, difficult to achieve requiring G>O(N^{2}) and p>0.5, where the parameter p captures a willingness for consensus. Allowing edge weights to be a consequence of attributes naturally captures homophily and reveals that many real-world social systems would have a subcritical number of attributes necessary to achieve structural balance.
主体间的相似性和连通三体中的结构平衡是被认为塑造社会群体的互补机制，导致例如共识或极化。为了以统一的方式捕捉这两个过程，我们提出了一种二元和三元相互作用的模型。我们考虑 N 个完全连接的主体，其中每个主体有 G 个潜在的属性，主体在属性空间中的相似性（即同质性）用于确定它们之间的链接权重。对于结构平衡，我们使用三元体更新规则，其中每个更新只故意改变一个主体的一个属性，但这也会导致链接权重甚至链接极性的意外变化。在 G 很大的极限下，链接权重动力学由福克-普朗克方程描述，从中可以得到过渡到所有链接均为正的完全平衡状态的条件。这种全局合作的“天堂状态”很难实现，需要 G>O(N^2)和 p>0.5，其中参数 p 捕获了对共识的意愿。允许边权重成为属性的结果自然地捕捉了同质性，并表明许多现实世界的社会系统需要有亚临界数量的属性来实现结构平衡。
