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1. Multidimensional attributes expose Heider balance dynamics to measurements

   https://doi.org/10.1038/s41598-023-42390-w  

   Linczuk, Joanna; Górski, Piotr J.; Szymanski, Boleslaw K.; Hołyst, Janusz A. (September 2023, Scientific Reports)

   Abstract Most of studied social interactions arise from dyadic relations. An exception is Heider Balance Theory that postulates the existence of triad dynamics, which however has been elusive to observe. Here, we discover a sufficient condition for the Heider dynamics observability: assigning the edge signs according to multiple opinions of connected agents. Using longitudinal records of university student mutual contacts and opinions, we create a coevolving network on which we introduce models of student interactions. These models account for: multiple topics of individual student opinions, influence of such opinions on dyadic relations, and influence of triadic relations on opinions. We show that the triadic influence is empirically measurable for static and dynamic observables when signs of edges are defined by multidimensional differences between opinions on all topics. Yet, when these signs are defined by a difference between opinions on each topic separately, the triadic interactions’ influence is indistinguishable from noise. 

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   Stengel-Eskin, E; Hase, P; Bansal, M (April 2025, Proceedings of the Nations of Americas Chapter of the Association for Computational Linguistics)
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   https://doi.org/10.7243/2055-2386-6-12  

   Thompson, Lara A (January 2019, Physical Therapy and Rehabilitation)
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   Schwartz, C (March 2025, The Centriod)