Lévy Walk Navigation in Complex Networks: A Distinct Relation between Optimal Transport Exponent and Network...

Area of Science:

• Network science
• Complex systems
• Statistical physics

Background:

• Lévy walk strategies are used for efficient diffusion on networks.
• Understanding how network properties influence diffusion is crucial.

Purpose of the Study:

• To investigate network navigation using a Lévy walk strategy.
• To determine the relationship between the optimal transport exponent and network fractal dimension.

Main Methods:

• Simulated diffusion processes on networks with Lévy walk strategies.
• Theoretically derived the relationship between the transport exponent and fractal dimension.
• Validated findings on synthetic and real-world networks.

Main Results:

• The optimal transport exponent (α(opt)) is determined by the fractal dimension (df) of the network.
• A new theoretical relation α(opt) = df + 2 was derived for synthetic networks.
• This relation was also observed in various real-world networks.

Conclusions:

• Network fractal dimension precisely governs efficient diffusion behavior.
• The derived relationship differs from previous models of network navigation.
• This work uncovers a new mechanism for efficient diffusion on diverse networks.