Enhancing structural balance theory and measurement to analyze signed digraphs of real-world social networks

Structural balance theory assumes triads in networks to gravitate toward stable configurations. The theory has been verified for undirected graphs. Since real-world social networks are often directed, we introduce a novel method for considering both transitivity and sign consistency for calculating balance in signed digraphs. We test our approach on graphs that we 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, balance is moderately high, ranging from 61% to 96%. This paper makes three contributions: First, we extend the theory of structural balance to include signed digraphs where both transitivity and sign consistency are required and considered for calculating balance in triads with signed and directed edges. This improves the modeling of communication networks and other organizational networks where ties might be directed. Second, we show how to construct and analyze email networks from unstructured text data, using natural language processing methods to infer two different types of edge signs from emails authored by nodes. Third, we empirically assess balance in two different and contemporary contexts, namely remote communication in two business organizations, and team-based interactions in a virtual environment. We find empirical evidence in support of structural balance theory across these contexts.