Structural Balance and Transitivity

Structural Balance is associated more with groups. Within a group there must be ties between the members of the group. A group is structurally balanced when the product of ties between all group members is positive. A positive tie is created by a 'like' relation between two group members, a negative one by a 'dislike' relation. If for example there are two negative ties and one positive tie the group is balanced, but if there is one negative and two positive ties the group is unbalanced. For example if two people like ice-cream then a "+" sign is shown representing a positive tie between the people. Now if two people in the group like chocolate ice-cream and the other likes vanilla, then only two have a positive bond and the group is not balanced. The social balance theory is based on people's theories of action, and these central concepts play a large role and deal with intrapersonal relation.

Often in social networks, positive and negative ties can represent friendly and unfriendly connections respectively. The structural balance of these networks are analyzed by the cycles contained within a single network. Continuing with the same definition, a cycle within a network is considered balanced if the product of the signs is positive. An entire graph or network is considered balanced if all the cycles contained within it are balanced. Under these circumstances, a balanced network tends to be a more stable while unbalanced networks tend to be unstable. It has been found through observation that network arrangements that are unbalanced will, over time, evolve into a more balanced state. From these patterns, it has become possible to predict the movement of a given social network.