Exact solution for mean first-passage time on a pseudofractal scale-free web

Area of Science:

• Complex Networks
• Statistical Physics
• Network Science

Background:

• Calculating mean first-passage time (MFPT) for trapping problems is challenging on complex media like real networks.
• Existing MFPT determinations are limited to simple structures such as regular lattices and geometric fractals.
• Real networks often exhibit scale-free and small-world properties, necessitating methods for analyzing random walks on such structures.

Purpose of the Study:

• To investigate random walks on a pseudofractal scale-free web (PSFW) with a central trap.
• To derive an exact solution for the MFPT on this complex network.
• To compare the transport efficiency of PSFW with other network structures.

Main Methods:

• Developed recurrence relations based on the PSFW structure to calculate MFPT.
• Obtained an exact analytical solution for the MFPT.
• Confirmed the analytical solution through direct numerical calculations.

Main Results:

• The MFPT on PSFW scales as a power-law function of the number of nodes, with an exponent less than 1.
• The PSFW structure demonstrates improved diffusion transport efficiency compared to regular lattices, Sierpinski fractals, and T-graphs.
• The derived analytical method is applicable to other deterministic networks for accurate MFPT computation.

Conclusions:

• The pseudofractal scale-free web offers an efficient medium for diffusion-based transport.
• The analytical approach provides a powerful tool for determining MFPT on complex deterministic networks.
• This study advances the understanding of random walks and transport phenomena in complex systems.