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Network growth with arbitrary initial conditions: degree dynamics for uniform and preferential attachment
Babak Fotouhi1, Michael G Rabbat1
1Department of Electrical and Computer Engineering McGill University, Montréal, Québec, Canada.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 4, 2014
Summary
This study presents time-dependent network growth models, accounting for initial conditions. It offers a flexible framework for analyzing evolving network structures under various attachment rules.
Area of Science:
- Network science
- Graph theory
- Statistical mechanics
Background:
- Understanding network evolution is crucial for various fields.
- Existing models often focus on long-term behavior, neglecting initial states.
- Network growth dynamics are influenced by attachment mechanisms and initial graph properties.
Purpose of the Study:
- To derive time-dependent expressions for the expected degree distribution in growing networks.
- To account for arbitrary initial conditions, unlike previous asymptotic-focused studies.
- To analyze the impact of uniform and preferential attachment with single/multiple link formation.
Main Methods:
- Developing analytical expressions for network degree distribution over time.
- Approximating node addition as a continuous arrival rate.
- Considering both uniform and preferential attachment models.
Main Results:
- Provided time-dependent formulas for expected degree distribution.
- Demonstrated that results align with previous asymptotic findings.
- The derived solution is dependent on the initial graph's degree distribution.
Conclusions:
- The study offers a comprehensive model for network growth dynamics.
- The framework is applicable to networks with arbitrary initial states.
- This work extends existing network growth theory by incorporating time-dependency and initial conditions.
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