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Structure of growing networks with preferential linking.
S N Dorogovtsev1, J F Mendes, A N Samukhin
1Departamento de Física and Centro de Física do Porto, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal. sdorogov@fc.up.pt
Physical Review Letters
|November 18, 2000
Summary
This study enhances network growth models by incorporating initial site attractiveness. The research reveals universal relationships between network exponents, offering insights into complex system dynamics.
Area of Science:
- Network Science
- Statistical Physics
- Complex Systems
Background:
- Growing network models often use preferential attachment, where new nodes connect to existing ones with more links.
- The influence of initial site characteristics on network evolution has been less explored.
Purpose of the Study:
- To generalize network growth models by including initial site attractiveness.
- To determine the exact stationary distribution of incoming links and the average connectivity over time.
- To uncover universal relationships between scaling exponents in evolving networks.
Main Methods:
- Mathematical modeling of network growth with preferential attachment and initial attractiveness.
- Derivation of the stationary distribution P(q) for incoming links.
- Calculation of the long-time limit of average connectivity q(s,t).
Main Results:
- The stationary distribution of incoming links follows P(q) ~ q^(-gamma) at long times, with gamma dependent on initial attractiveness.
- The average connectivity q(s,t) scales as (s/t)^(-beta) at long times.
- A universal relationship beta(gamma-1) = 1 was established between the exponents gamma and beta.
Conclusions:
- Initial site attractiveness significantly impacts the structure of growing networks.
- The derived universal exponent relation provides fundamental insights into the dynamics of complex evolving systems.
- The generalized model offers a more comprehensive understanding of real-world network formation.