ABSTRACT In a fully connected network of K individuals, links represent symmetric interpersonal relations with their signs – positive for friendly, negative for hostile ones. The network is balanced in the sense of Heider if it is divided into two, internally friendly but mutually hostile groups. A dynamics of the relations has been proposed which leads to balanced states; there, a separate differential equation is designed for each out of K(K-1)/2 links. Here we demonstrate that besides the balanced states, whole families of stable-unbalanced states exist, and the number of these states is limited only by the size of the network. Examples are given for three and four internally friendly, but mutually hostile groups.

中文翻译：

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海德平衡、偏见和尺寸效应

摘要 在一个由 K 个个体组成的完全连接的网络中，链接代表与其符号的对称人际关系 - 积极代表友好，消极代表敌对。如果网络被分成两个内部友好但相互敌对的群体，则网络在 Heider 的意义上是平衡的。已经提出了导致平衡状态的关系动态；在那里，为 K(K-1)/2 个链接中的每一个设计了一个单独的微分方程。在这里，我们证明除了平衡状态之外，还存在整个稳定-不平衡状态族，并且这些状态的数量仅受网络规模的限制。给出了三个和四个内部友好但相互敌对的团体的例子。