Random walks on non-homogenous weighted Koch networks

Area of Science:

• Complex Networks
• Network Science
• Traffic Systems Modeling

Background:

• Weighted Koch networks are fractal structures with applications in modeling complex systems.
• Understanding information propagation and traversal times in networks is crucial for system efficiency.
• Existing models often simplify network topology and weighting schemes.

Purpose of the Study:

• To introduce and analyze new models of non-homogenous weighted Koch networks.
• To define and investigate the average weighted receiving time (AWRT) in these networks.
• To determine the relationship between network order and AWRT, and analyze average weighted shortest path (AWSP).

Main Methods:

• Development of non-homogenous weighted Koch network models with three scaling factors (r1, r2, r3).
• Definition of Average Weighted Receiving Time (AWRT) inspired by Average Weighted Shortest Path (AWSP).
• Analysis of walker movement dynamics assuming uniform probability to move to any neighbor.

Main Results:

• The AWRT exhibits a power-law relationship with the network order in large networks.
• The exponent of this power-law is determined by the scaling factors: θ(r1, r2, r3) = log4(1 + r1 + r2 + r3).
• The AWSP, in the infinite network order limit, is solely dependent on the sum of the scaling factors (r1 + r2 + r3).

Conclusions:

• The proposed non-homogenous weighted Koch network models provide a more realistic representation of traffic systems.
• The derived AWRT scaling law offers a predictive tool for network performance.
• The findings contribute to the understanding of traversal dynamics in complex, weighted fractal networks.