A PARTITIONING APPROACH TO STRUCTURAL BALANCE

The classic formulation of structural balance by Cartwright and Harary (Psychological Review, 63, 1956, 277-293) had the basic structural th eorem that a balanced structure could be partitioned into two mutually antagonistic subgroups each having internal solidarity. Davis (Human Relations, 20, 1967, 181-187) extended this theorem for cases where th ere can be more than two such mutually antagonistic subgroups. We use these theorems to construct a criterion function for a local optimizat ion partitioning procedure for signed digraphs. For any signed digraph , this procedure yields those partitions with the smallest number of e rrors, a measure of the imbalance in the graph, and an identification of those links inconsistent with both generalized and structural balan ce. These methods are applied to some artificial data and to the affec t data from Sampson (A novitiate in a period of change: An experimenta l and case study of social relationships, Dissertation, Cornell Univer sity, 1968). The latter provides a positive test of a basic tenet of b alance theory, that there is a tendency towards balance with signed re lations in human groups. While these methods can be applied to all sig ned digraphs and signed graphs, the balance hypothesis is relevant onl y for affect ties.