Random spreading phenomena in annealed small world networks

Abstract

We study the simple random walk dynamics on an annealed version of a Small-World Network (SWN) consisting of $N$ nodes. This is done by calculating the mean number of distinct sites visited S(n) and the return probability $P_{00}(t)$ as a function of the time $t$. $S(t)$ is a key quantity both from the statistical physics point of view and especially for characterizing the efficiency of the network connectedness. Our results for this quantity shows features similar to the SWN with quenched disorder, but with a crossover time that goes inversely proportianal to the probability $p$ of making a long range jump instead of being proportional to $p^{-2}$ as in quenched case. We have also carried out simulations on a modified annealed model where the crossover time goes as $p^{-2}$ due to specific time dependent transition probabilities and we present an approximate self-consistent solution to it.

References in corpus (3)

• Statistical mechanics of complex networks
• Spectra of "Real-World" Graphs: Beyond the Semi-Circle Law
• Scaling of random spreading in small world networks

Cited by in corpus (6)

• The structure and function of complex networks
• Evolution of networks
• Solution of voter model dynamics on annealed small-world networks
• Scaling Properties of Random Walks on Small-World Networks
• Optimal disorder for segregation in annealed small worlds
• Diffusion Processes on Small-World Networks with Distance-Dependent Random-Links