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Random initial condition in small Barabasi-Albert networks and deviations from the scale-free behavior
Paulo R Guimarães1, Marcus A M de Aguiar, Jordi Bascompte
1Instituto de Biologia, Universidade Estadual de Campinas (UNICAMP), SP, Brazil.
Summary
The initial core size and connectivity in Barabasi-Albert networks significantly influence network topology. These factors determine whether scale-free networks exhibit broad or single-scale degree distributions.
Area of Science:
- Network Science
- Complex Systems
Background:
- Barabasi-Albert networks are a fundamental model for generating scale-free networks.
- Preferential attachment is the core mechanism for node addition in these networks.
Purpose of the Study:
- To investigate how the initial core's size and average connectivity affect the topology of small scale-free networks.
- To understand the impact of initial conditions on degree distribution tails.
Main Methods:
- Simulations of Barabasi-Albert network growth.
- Analysis of network topology as a function of initial core parameters.
Main Results:
- Initial core size and connectivity strongly influence the tail of the degree distribution.
- These parameters can lead to either broad-scale or single-scale network properties.
- Exponential truncation of power-law behavior in small scale-free networks is linked to initial core characteristics.
Conclusions:
- The size and density of connections in the initial network core are critical determinants of scale-free network topology.
- Understanding these initial parameters is key to explaining variations in degree distribution observed in small scale-free networks.
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