Structural balance in signed digraphs: considering transitivity to measure balance in graphs constructed by using different link signing methods

TL;DR

This paper introduces a new method for measuring structural balance in signed directed graphs by incorporating transitivity and sign consistency, tested on graphs derived from text and survey data, revealing moderate to high balance levels.

Contribution

The paper presents a novel approach to assess balance in signed digraphs considering transitivity, extending structural balance theory to directed networks with real-world data applications.

Findings

Balance ranges from 67.5% to 92.4% across different contexts.

The method effectively captures balance in directed signed networks.

Results are consistent across various sign detection methods.

Abstract

Structural balance theory assumes triads in networks to gravitate towards stable configurations. The 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 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 67.5% to 92.4%.