Structural Balance via Gradient Flows Over Signed Graphs

• 成果类型: Article
• 署名作者: Cisneros-Velarde, Pedro Arturo; Friedkin, Noah E.; Proskurnikov, Anton, V; Bullo, Francesco
• 署名单位: University of California System; University of California Santa Barbara; Polytechnic University of Turin; Russian Academy of Sciences
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3018435
• 发表日期: 2021
• 页码: 3169-3183
• 关键词: Appraisal; Numerical models; Mathematical model; computational modeling; CONVERGENCE; Analytical models; dynamical systems; gradient flow; signed network; social dynamics; structural balance

摘要

Structural balance is a classic property of signed graphs satisfying Heider's seminal axioms. Mathematical sociologists have studied balance theory since its inception in the 1940s. Recent research has focused on the development of dynamic models explaining the emergence of structural balance. In this article, we introduce a novel class of parsimonious dynamic models for structural balance based on an interpersonal influence process. Our proposed models are gradient flows of an energy function, called the dissonance function, which captures the cognitive dissonance arising from the violations of Heider's axioms. Thus, we build a new connection with the literature on energy landscape minimization. This gradient-flow characterization allows us to study the transient and asymptotic behaviors of our model. We provide mathematical and numerical results describing the critical points of the dissonance function.