What is special about diffusion on scale-free nets?

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. 3 Author to whom all correspondence should be addressed. New Journal of Physics 7 (2005) 26 PII: S1367-2630(05)87279-9 1367-2630/05/010026+21$30.00 © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft 2 DEUTSCHE PHYSIKALISCHE GESELLSCHAFT