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What is Special about Diffusion on Scale-Free Nets?

Erik M. Bollt·Daniel ben-Avraham
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Abstract

We study diffusion (random walks) on recursive scale-free graphs, and contrast the results to similar studies in other analytically soluble media. This allows us to identify ways in which diffusion in scale-free graphs is special. Most notably, scale-free architecture results in a faster transit time between existing nodes, when the network grows in size; and walks emanating from the most connected nodes are recurrent, despite the network's infinite dimension. We also find that other attributes of the graph, besides its scale-free distribution, have a strong influence on the nature of diffusion.

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Erik M. Bollt, Daniel ben-Avraham. 2004-10-19. What is Special about Diffusion on Scale-Free Nets?. https://arxiv.org/abs/cond-mat/0409465

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