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Structural balance in one time step

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  • Krawczyk, Malgorzata J.
  • Kułakowski, Krzysztof

Abstract

In complete graphs with signed links, the structural balance means that the graph nodes are divided into two groups, internally friendly (positive links) and mutually hostile (negative links). We present a simple formula which, for any initial condition, allows to reach the structural balance in one time step. The formula works for complete graphs of odd number of nodes.

Suggested Citation

  • Krawczyk, Malgorzata J. & Kułakowski, Krzysztof, 2022. "Structural balance in one time step," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 606(C).
    • Handle: RePEc:eee:phsmap:v:606:y:2022:i:c:s0378437122007117
    DOI: 10.1016/j.physa.2022.128153
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    References listed on IDEAS

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    1. Hassanibesheli, Forough & Hedayatifar, Leila & Gawroński, Przemysław & Stojkow, Maria & Żuchowska-Skiba, Dorota & Kułakowski, Krzysztof, 2017. "Gain and loss of esteem, direct reciprocity and Heider balance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 334-339.
    2. Hannah Weinmann & Krzysztof Kułakowski & Alfio Borzì, 2022. "Ecosystem models and social balance from a synchronization perspective," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 33(05), pages 1-29, May.
    3. Michael T. SCHAUB & Neave O'CLERY & Yazan N. BILLEH & Jean-Charles DELVENNE & Renaud LAMBIOTTE & Mauricio BARAHONA, 2016. "Graph partitions and cluster synchronization in networks of oscillators," LIDAM Reprints CORE 2886, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Krzysztof Kułakowski & Przemysław Gawroński & Piotr Gronek, 2005. "The Heider Balance: A Continuous Approach," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 16(05), pages 707-716.
    5. Krawczyk, Małgorzata J. & del Castillo-Mussot, Marcelo & Hernández-Ramírez, Eric & Naumis, Gerardo G. & Kułakowski, Krzysztof, 2015. "Heider balance, asymmetric ties, and gender segregation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 439(C), pages 66-74.
    6. Sun, Yixiang & Du, Haifeng & Gong, Maoguo & Ma, Lijia & Wang, Shanfeng, 2014. "Fast computing global structural balance in signed networks based on memetic algorithm," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 415(C), pages 261-272.
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