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Topology and correlations in structured scale-free networks
Alexei Vázquez1, Marián Boguñá, Yamir Moreno
1International School for Advanced Studies and INFM, Via Beirut 4, Trieste I-34014, Italy.
Summary
We analyzed scale-free networks with high clustering. Connectivity probability distribution depends on model details, and small-world properties are absent across the parameter range.
Area of Science:
- Network Science
- Complex Systems Analysis
- Statistical Physics
Background:
- Scale-free networks are crucial in modeling complex systems.
- A recently introduced class exhibits high clustering and connectivity correlations.
- Understanding their detailed properties is essential for accurate modeling.
Purpose of the Study:
- To investigate a novel class of scale-free networks.
- To analyze the connectivity probability distribution and its dependence on model specifics.
- To determine the presence or absence of small-world properties.
Main Methods:
- Exact solution for low average connectivity scenarios.
- Derivation of exact expressions for clustering and degree correlation functions.
- Detailed analysis of network properties across the parameter range.
Main Results:
- Connectivity probability distribution is highly sensitive to model details.
- Exact expressions for clustering and degree correlation functions were obtained.
- The studied networks lack small-world properties universally.
Conclusions:
- The fine details of the model critically influence network connectivity.
- The absence of small-world properties is a key characteristic of this network class.
- Further analysis provides insights into the physical properties of these networks.