The Fractional Preferential Attachment Scale-Free Network Model.

Area of Science:

• Network Science
• Complex Systems
• Statistical Physics

Background:

• Natural networks often exhibit preferential attachment and scale-free properties.
• The Barabási-Albert (BA) model is a foundational scale-free network model based on preferential attachment.

Purpose of the Study:

• To introduce a generalized scale-free network model called Fractional Preferential Attachment (FPA).
• To investigate the impact of the 'f' parameter on network properties.
• To compare FPA networks with existing synthetic and real-world networks.

Main Methods:

• Developing the Fractional Preferential Attachment (FPA) model, a generalization of the Barabási-Albert model.
• Numerically generating networks using the FPA model with varying 'f' parameter values (f ∈ (0, 1]).
• Analyzing topological properties including degree distribution, degree correlation, clustering coefficient, and network diameter.

Main Results:

• The FPA model generates scale-free networks with time-independent degree distributions (p(k) ∼ k⁻γ, 2 < γ ≤ 3).
• The 'f' parameter significantly influences network properties like degree distribution and correlation.
• FPA networks exhibit parameters comparable to real-world networks, depending on the 'f' value.
• FPA networks were found to be non-fractal, irrespective of the 'f' parameter.

Conclusions:

• The FPA model provides a flexible and tunable approach to generating scale-free networks.
• It serves as a valuable alternative to existing network models due to its ability to mimic real-world network characteristics.
• The 'f' parameter offers a novel way to control network topology and statistical properties.