Heider balance, prejudices and size effect

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.

KEYWORDS:

• Structural balance
• model
• complete network