What is Special about Diffusion on Scale-Free Nets?

TL;DR

This paper investigates how diffusion processes behave uniquely on recursive scale-free networks, highlighting faster transit times and recurrence from hubs, influenced by the network's structure beyond its degree distribution.

Contribution

It identifies specific diffusion characteristics on scale-free graphs, such as faster transit and hub recurrence, contrasting with other media and emphasizing structural influences.

Findings

Faster transit times in growing scale-free networks.

Recurrence of walks from highly connected nodes.

Other graph attributes significantly influence diffusion.

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.