Self-attracting walk on heterogeneous networks.

Area of Science:

• Complex systems
• Network science
• Information science

Background:

• Human mobility in cyberspace is crucial in the information era.
• While understood in Euclidean space, mobility in random networks like the WWW remains elusive.
• This study focuses on self-attracting walks on scale-free networks.

Purpose of the Study:

• To investigate the diffusion characteristics of self-attracting walks on scale-free networks.
• To understand how memory-dependent mobility affects exploration in heterogeneous networks.
• To analyze the impact of self-attraction on human mobility patterns in online environments.

Main Methods:

• Simulating self-attracting walks on scale-free network models.
• Analyzing the growth of distinct visited nodes over time.
• Investigating the characteristic volumes and topology of visited node clusters.
• Deriving scaling exponents to characterize diffusion dynamics.

Main Results:

• Under strong attraction, distinct nodes grow linearly with time, faster in heterogeneous networks.
• Crossovers to sublinear growth are observed in strongly heterogeneous networks.
• Reinforced attraction to hubs initially expedites exploration but later delays it.

Conclusions:

• Self-attracting walks exhibit complex diffusion behaviors in heterogeneous networks.
• Network topology and walker's memory significantly influence exploration dynamics.
• The findings offer insights into human mobility patterns and diffusion processes online.