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Diffusion-limited friendship network: a model for six degrees of separation
1Satyendra Nath Bose National Centre for Basic Sciences Block-JD, Sector-III, Salt Lake, Kolkata 700098, India.
Summary
This study models social networks using random walkers and random graphs, revealing a phase transition. Introducing birth and death rates maintains the "six degrees of separation" social network structure.
Area of Science:
- Sociophysics
- Network Science
- Computational Social Science
Background:
- Societies can be modeled as complex networks.
- Understanding social dynamics and disease spread is crucial.
Purpose of the Study:
- To develop a dynamic model of a society using random walkers and random graphs.
- To investigate the impact of birth and death rates on social network structure.
- To analyze disease propagation within this dynamic social network.
Main Methods:
- Utilizing a dynamic model where individuals are uncorrelated random walkers.
- Representing the social network as a dynamical random graph.
- Applying a susceptible-infected-susceptible (SIS) model for disease spread analysis.
Main Results:
- The social network exhibits a percolation-like phase transition.
- The 'six degrees of separation' phenomenon persists with simultaneous birth and death rates.
- Network diameter is influenced by the death/birth rate.
- Disease spread is limited below a critical population density threshold.
Conclusions:
- Dynamic social networks demonstrate robust structural properties like 'six degrees of separation'.
- Population dynamics (birth/death rates) modulate network characteristics.
- Societal health is maintainable through population density control, preventing widespread disease.
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