On the measurement of structural balance

If in a group of people every one loves his friends' friends and also his enemies' enemies and hates his friends' enemies and his enemies' friends, the “signed graph” representing the network of relations will be balanced. The degree of balance of a graph, then, provides a sociometric index which may be of importance in constructing theories of group structure and behavior. There are several ways of defining the degree of balance, and the group has several ways of altering this index, for example by reversing existing relationships, by deleting them, or by expelling members. There may be tendencies other than toward balance operating in a group, and these may be opposed to each other. This paper continues the exploration of the mathematical properties of signed graphs with special reference to specific assumptions about the evolution of human groups.