Diffusion in scale-free networks with annealed disorder

Abstract

The scale-free (SF) networks that have been studied so far contained quenched disorder generated by random dilution which does not vary with the time. In practice, if a SF network is to represent, for example, the worldwide web, then the links between its various nodes may temporarily be lost, and re-established again later on. This gives rise to SF networks with annealed disorder. Even if the disorder is quenched, it may be more realistic to generate it by a dynamical process that is happening in the network. In this paper, we study diffusion in SF networks with annealed disorder generated by various scenarios, as well as in SF networks with quenched disorder which, however, is generated by the diffusion process itself. Several quantities of the diffusion process are computed, including the mean number of distinct sites visited, the mean number of returns to the origin, and the mean number of connected nodes that are accessible to the random walkers at any given time. The results including, (1) greatly reduced growth with the time of the mean number of distinct sites visited; (2) blocking of the random walkers; (3) the existence of a phase diagram that separates the region in which diffusion is possible from one in which diffusion is impossible, and (4) a transition in the structure of the networks at which the mean number of distinct sites visited vanishes, indicate completely different behavior for the computed quantities than those in SF networks with quenched disorder generated by simple random dilution.

18 pages including 8 figures

References in corpus (6)

• Stability and topology of scale-free networks under attack and defense strategies
• Absence of kinetic effects in reaction-diffusion processes in scale-free networks
• Random walk and trapping processes on scale-free networks
• The Krause-Hegselmann Consensus Model with Discrete Opinions
• Optimal disorder for segregation in annealed small worlds
• Random Walks on Complex Networks

Cited by in corpus (12)

• Epidemic processes in complex networks
• Random walks and diffusion on networks
• Epidemic thresholds of the Susceptible-Infected-Susceptible model on networks: A comparison of numerical and theoretical results
• Fractal and Transfractal Recursive Scale-Free Nets
• Langevin approach for the dynamics of the contact process on annealed scale-free networks
• Exploring Complex Networks through Random Walks
• Mean-field diffusive dynamics on weighted networks
• Random walks on complex trees
• Epidemic Threshold in Continuous-Time Evolving Networks
• Generation of arbitrarily two-point correlated random networks
• Phase transitions with infinitely many absorbing states in complex networks
• Detecting Structure of Complex Network by Quantum Bosonic Dynamics