In social network theory, a community of individuals characterized by friendly/hostile relationships is usually modeled as a signed graph having the individuals as nodes and their pairwise relationships as edges: an edge of positive weight expresses friendship, one of negative weight aversion or hostility [1,2]. According to Heider’s theory of structural balance [3], in a balanced community the role of friends and enemies, determined locally by the bipartite relationships, is perfectly defined also on triads and is equivalent to all length-3 cycles having the positive sign. Since the sign of a cycle is the product of the signs of its edges, a positive sign corresponds to an even number of negative edges along a cycle. Heider’s original definition for triads can be generalized to larger groups of individuals using the graph theoretical formulation of Cartwright and Harary [4]: the lack of structural tensions corresponds to all cycles of the signed graph being positive. Also for this more general definition (the one adopted in this paper) structural balance implies a lack of ambiguity in the way each individual classifies another individual as a friend or as an enemy. An equivalent characterization is in fact that the network splits into two factions such that each faction contains only friendly relationships while individuals belonging to different factions are linked only by antagonistic relationships.
ፍትህ ለሁሉም / Justice for All