Structural balance in complex network: Observation, Emergence and Implications

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Abstract

Since its first conceptualization in psychology, the theory of Structural balance was extended to economics, ecology and social science. Trespassing disciplinary boundaries, one of its first simple network formulations posits that triangles in signed networks should have an even number of negative links. This very simple statement has two significant consequences. First, it strongly affects our expectations about the macroscopic structure and functioning of an analyzed system. Second, it allows us to define specific dynamics at the microscopic level, i.e., different rules for describing the evolution of signed relations between system elements.

From its first formulation, multiple measures, many algorithmically advanced, have been proposed to quantify structural balance. However, these measures may be at odds with each other and give different perspectives on the status of an analyzed system. Sometimes, these differences are intended to capture different nuances of the micro-rule originating the structural balance. Other times, they are unintended and depend on different (unconscious) understandings of the system itself.

Connected to this first observability problem, there are two other central problems. First, the emergence of structural balance as a macroscopic property can be obtained by other theories with different (but compatible) microscopic rules. This fact raises the question: Is structural balance theory and its dynamics needed to model systems? Second, there are contradicting results about how the SB dynamics and macroscopic properties arising from it affect a system’s performance. For instance, structural balance in traders’ affective relations positively impacts their performance. Conversely, structural balance in the relations of Wikipedia contributors negatively impacts the quality of the edited articles. This type of opposite findings keeps the discussion about the link between structural balance and performance open, raising the question: Is structural balance good or bad in real-world systems?

By touching on these topics and questions, I will delve into the discussion regarding the observation, emergence and implications of structural balance to understand its role in complex systems.

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