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Stability in social networks.

Santanu Acharjee1, Amlanjyoti Oza1

  • 1Department of Mathematics, Gauhati University, Guwahati 781014, Assam, India.

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Summary
This summary is machine-generated.

This study examines Dunbar's number from a couple's perspective, revealing that maintaining a stable relationship minimally impacts one's social network size. Mathematical analysis shows friendship stability is possible even with limited partner interaction.

Keywords:
Dunbar’s numberdivorcefriendshipmarriagesocial networkssoft set

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Area of Science:

  • Social network analysis
  • Evolutionary psychology
  • Mathematical sociology

Background:

  • Dunbar's number, a cognitive limit of 150 stable relationships, is typically studied from an individual perspective.
  • Existing research on Dunbar's number and social networks lacks a systems-level analysis of couples.
  • The impact of romantic relationships on social network structure and stability is not well-understood.

Purpose of the Study:

  • To analyze the impact of Dunbar's number and hierarchy on couples as a system.
  • To mathematically model the conjoint social network of a couple.
  • To assess the stability of personal social networks within romantic relationships.

Main Methods:

  • Mathematical modeling of conjoint Dunbar graphs for couples.
  • Application of soft set theory to social network stability.
  • Utilizing a balance theoretic approach to analyze relationship dynamics.

Main Results:

  • Entering a romantic relationship may incur a 'cost of romance,' potentially reducing one's support network by two individuals.
  • Mathematical analysis indicates that minimal time spent with a partner does not significantly alter existing friendships.
  • The study models how social network structure evolves during a romantic relationship.

Conclusions:

  • A couple can be analyzed as a distinct social system in relation to Dunbar's number.
  • Social network stability within romantic relationships can be mathematically assessed.
  • Findings contribute to understanding relationship dynamics and social network resilience.