Average trapping time on weighted directed Koch network.

Area of Science:

• Complex Networks
• Network Science
• Statistical Physics

Background:

• Random walks on undirected networks are well-studied.
• Random walks on weighted directed networks, especially with a target node, are less understood.
• Scale-free networks are crucial in modeling real-world systems.

Purpose of the Study:

• To investigate random walks on weighted directed scale-free networks.
• To evaluate transportation efficiency using average trapping time (ATT).
• To introduce and analyze directed weighted Koch networks.

Main Methods:

• Introduction of directed weighted Koch networks with tunable edge weights (θ).
• Derivation of an exact solution for average trapping time (ATT).
• Inclusion of a delay parameter (p) to modify transition probabilities and derivation of a closed-form solution for ATT.

Main Results:

• The average trapping time (ATT) depends on the weight parameter θ.
• ATT can exhibit sub-linear, linear, or super-linear growth with θ.
• The delay parameter p affects the ATT's coefficient but not its leading behavior.
• Simultaneous tuning of θ and p allows control over ATT and trapping efficiency.

Conclusions:

• This work advances the understanding of random walks on directed weighted scale-free networks.
• The derived solutions provide insights into network transportation efficiency.
• The findings offer methods to optimize network performance through parameter control.