Structural balance in real-world social networks: incorporating direction and transitivity in measuring partial balance

Structural balance theory predicts that triads in networks gravitate towards stable configurations. This theory has been verified for undirected graphs. Since real-world networks are often directed, we introduce a novel method for considering both transitivity and sign consistency for evaluating partial balance in signed digraphs. We test our approach on graphs constructed by using different methods for identifying edge signs: natural language processing to infer signs from underlying text data, and self-reported survey data. Our results show that for various social contexts and edge sign detection methods, partial balance of these digraphs is moderately high, ranging from 61 to 96%. Our approach not only enhances the theoretical framework of structural balance but also provides practical insights into the stability of social networks, enabling a deeper understanding of interpersonal and group dynamics across different communication platforms.