Related Experiment Videos
Weighted scale-free networks with stochastic weight assignments
Dafang Zheng1, Steffen Trimper, Bo Zheng
1Fachbereich Physik, Martin-Luther-Universität, D-06099 Halle, Germany.
Summary
We developed a weighted scale-free network model where link weights depend on node popularity and fitness. Increasing the influence of fitness on link formation reduces the power-law exponent for total network weight.
Area of Science:
- Network Science
- Statistical Physics
- Complex Systems
Background:
- Scale-free networks are ubiquitous in nature and technology.
- Understanding the role of link weights is crucial for network analysis.
- Existing models often simplify weight assignment mechanisms.
Purpose of the Study:
- To introduce a novel model for weighted scale-free networks.
- To investigate the impact of node popularity and fitness on link weights.
- To analyze the resulting weight distribution and scaling properties.
Main Methods:
- Development of a stochastic model for link weight assignment.
- Incorporation of connectivity and fitness probabilities (p and 1-p).
- Derivation of an analytical expression for total weight.
- Numerical simulations to validate analytical findings.
Main Results:
- The total weight distribution follows a power law with exponent sigma.
- Exponent sigma is dependent on the probability p, decreasing as p increases.
- For p=0, scaling matches connectivity distribution.
- A generalized model with fitness-dependent link formation was explored.
Conclusions:
- The proposed model offers a more realistic representation of weighted networks.
- Node fitness significantly influences network weight distribution and scaling.
- The analytical framework provides insights into complex network dynamics.