Generalized degree-biased random walk on scale-free networks

Area of Science:

• Network Science
• Complex Systems Analysis
• Computational Modeling

Background:

• Scale-free networks are ubiquitous in nature and technology.
• Traditional random walk models struggle with efficiency in sparse networks.
• Hub-leaf trapping motifs hinder efficient network exploration.

Purpose of the Study:

• To develop a generalized degree-biased random walk (GDBRW) model for scale-free networks.
• To enhance network exploration efficiency, particularly in low-connectivity regimes.
• To suppress detrimental motifs like hub-leaf trapping.

Main Methods:

• Developing a GDBRW model with tunable exponents (α, β) for transition probabilities.
• Deriving equilibrium probability distributions using a continuum approach.
• Simulating exploration times across various network densities.

Main Results:

• The GDBRW model significantly improves exploration efficiency in sparse networks.
• It outperforms traditional popularity-driven random walks.
• The model effectively suppresses fallbacks and hub-leaf trapping motifs.

Conclusions:

• GDBRW offers a robust and efficient strategy for exploring scale-free networks.
• The model's effectiveness is particularly pronounced in low-connectivity environments.
• Symmetry-driven suppression of fallbacks is key to improved coverage efficiency.