Evidence of equilibrium dynamics in human social networks evolving in time

Abstract How do networks of social relationships evolve over time? This study addresses the lack of longitudinal analyses of social networks grounded in mathematical modelling. We analyse a dataset tracking the social interactions of 900 individuals over four years. Despite shifts in individual rela...

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Main Authors: Miguel A. González-Casado, Andreia Sofia Teixeira, Angel Sánchez
Format: Article
Language:English
Published: Nature Portfolio 2025-06-01
Series:Communications Physics
Online Access:https://doi.org/10.1038/s42005-025-02156-4
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author Miguel A. González-Casado
Andreia Sofia Teixeira
Angel Sánchez
author_facet Miguel A. González-Casado
Andreia Sofia Teixeira
Angel Sánchez
author_sort Miguel A. González-Casado
collection DOAJ
description Abstract How do networks of social relationships evolve over time? This study addresses the lack of longitudinal analyses of social networks grounded in mathematical modelling. We analyse a dataset tracking the social interactions of 900 individuals over four years. Despite shifts in individual relationships, the macroscopic structure of the network remains stable, fluctuating within predictable bounds. We link this stability to the concept of equilibrium in statistical physics. Specifically, we show that the probabilities governing link dynamics are stationary over time, and that key network features align with equilibrium predictions. Moreover, the dynamics also satisfy the detailed balance condition. This equilibrium persists despite ongoing turnover, as individuals join, leave, and shift connections. This suggests that equilibrium arises not from specific individuals but from the balancing act of human needs, cognitive limits, and social pressures. Practically, this equilibrium simplifies data collection, supports methods relying on single network snapshots (like Exponential Random Graph Models), and aids in designing interventions for social challenges. Theoretically, it offers insights into collective human behaviour, revealing how emergent properties of complex social systems can be captured by simple mathematical models.
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spelling doaj-art-900975ee8c4e4e75a30c3dc9170fbd1a2025-08-20T03:10:37ZengNature PortfolioCommunications Physics2399-36502025-06-018111310.1038/s42005-025-02156-4Evidence of equilibrium dynamics in human social networks evolving in timeMiguel A. González-Casado0Andreia Sofia Teixeira1Angel Sánchez2Grupo Interdisciplinar de Sistemas Complejos (GISC), Departamento de Matemáticas, Universidad Carlos III de MadridNetwork Science Institute, Northeastern University LondonGrupo Interdisciplinar de Sistemas Complejos (GISC), Departamento de Matemáticas, Universidad Carlos III de MadridAbstract How do networks of social relationships evolve over time? This study addresses the lack of longitudinal analyses of social networks grounded in mathematical modelling. We analyse a dataset tracking the social interactions of 900 individuals over four years. Despite shifts in individual relationships, the macroscopic structure of the network remains stable, fluctuating within predictable bounds. We link this stability to the concept of equilibrium in statistical physics. Specifically, we show that the probabilities governing link dynamics are stationary over time, and that key network features align with equilibrium predictions. Moreover, the dynamics also satisfy the detailed balance condition. This equilibrium persists despite ongoing turnover, as individuals join, leave, and shift connections. This suggests that equilibrium arises not from specific individuals but from the balancing act of human needs, cognitive limits, and social pressures. Practically, this equilibrium simplifies data collection, supports methods relying on single network snapshots (like Exponential Random Graph Models), and aids in designing interventions for social challenges. Theoretically, it offers insights into collective human behaviour, revealing how emergent properties of complex social systems can be captured by simple mathematical models.https://doi.org/10.1038/s42005-025-02156-4
spellingShingle Miguel A. González-Casado
Andreia Sofia Teixeira
Angel Sánchez
Evidence of equilibrium dynamics in human social networks evolving in time
Communications Physics
title Evidence of equilibrium dynamics in human social networks evolving in time
title_full Evidence of equilibrium dynamics in human social networks evolving in time
title_fullStr Evidence of equilibrium dynamics in human social networks evolving in time
title_full_unstemmed Evidence of equilibrium dynamics in human social networks evolving in time
title_short Evidence of equilibrium dynamics in human social networks evolving in time
title_sort evidence of equilibrium dynamics in human social networks evolving in time
url https://doi.org/10.1038/s42005-025-02156-4
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