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Walk with Me Hybrid Virtual/In-Person Walking for Older Adults with Neurodegenerative Disease

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Generalized degree-biased random walk on scale-free networks.

Karan Singh¹, Narendran R V¹, V K Chandrasekar²

¹Indian Institute of Science Education and Research Thiruvananthapuram, School of Physics, Thiruvananthapuram 695551, Kerala, India.

Physical Review. E

|January 21, 2026

Summary

We introduce a generalized degree-biased random walk (GDBRW) model for scale-free networks. This model enhances exploration efficiency, especially in sparse networks, by suppressing common trapping motifs.

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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.