Diffusion in scale-free networks with annealed disorder.

Area of Science:

• Complex Networks
• Statistical Physics
• Network Science

Background:

• Traditional scale-free (SF) networks often assume quenched disorder, where network structure is static.
• Real-world networks, like the World Wide Web, exhibit dynamic changes, leading to annealed disorder.
• Dynamical processes within networks can also generate disorder, even if it appears quenched.

Purpose of the Study:

• To investigate diffusion dynamics in SF networks with annealed disorder.
• To explore diffusion in SF networks where disorder arises from the diffusion process itself.
• To compare these dynamics against SF networks with static, randomly diluted disorder.

Main Methods:

• Simulating diffusion processes on SF networks with various annealed disorder scenarios.
• Analyzing SF networks with quenched disorder generated by diffusion dynamics.
• Computing key diffusion metrics: mean distinct sites visited, mean returns to origin, and accessible connected nodes.

Main Results:

• Observed greatly reduced growth in the mean number of distinct sites visited over time.
• Identified "blocking" phenomena that impede random walkers.
• Established a phase diagram indicating regions of possible and impossible diffusion.
• Detected a network structural transition where the mean distinct sites visited collapses.

Conclusions:

• Diffusion in SF networks with annealed or dynamically generated disorder differs fundamentally from those with static quenched disorder.
• The observed blocking and phase transitions highlight unique behaviors in dynamic network environments.
• These findings have implications for understanding information propagation and transport in evolving complex systems.