A partitioning approach to structural balance

Abstract

The classic formulation of structural balance by Cartwright and Harary (Psychological Review, 63, 1956, 277–293) had the basic structural theorem 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 there can be more than two such mutually antagonistic subgroups. We use these theorems to construct a criterion function for a local optimization partitioning procedure for signed digraphs. For any signed digraph, this procedure yields those partitions with the smallest number of errors, a measure of the imbalance in the graph, and an identification of those links inconsistent with both generalized and structural balance. These methods are applied to some artificial data and to the affect data from Sampson (A novitiate in a period of change: An experimental and case study of social relationships, Dissertation, Cornell University, 1968). The latter provides a positive test of a basic tenet of balance theory, that there is a tendency towards balance with signed relations in human groups. While these methods can be applied to all signed digraphs and signed graphs, the balance hypothesis is relevant only for affect ties.