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.

[1]  T. Aste,et al.  Innovation flow through social networks: productivity distribution in France and Italy , 2004 .

[2]  S. N. Dorogovtsev,et al.  Pseudofractal scale-free web. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Albert-Laszlo Barabasi,et al.  Deterministic scale-free networks , 2001 .

[4]  Cohen,et al.  Resilience of the internet to random breakdowns , 2000, Physical review letters.

[5]  D. Sherrington.  Stochastic Processes in Physics and Chemistry , 1983 .

[6]  S. N. Dorogovtsev,et al.  Evolution of networks , 2001, cond-mat/0106144.

[7]  Sidney Redner,et al.  A guide to first-passage processes , 2001 .

[8]  L. Gallos,et al.  Absence of kinetic effects in reaction-diffusion processes in scale-free networks. , 2004, Physical review letters.

[9]  Sidney Redner,et al.  Scaling of the first-passage time and the survival probability on exact and quasi-exact self-similar structures , 1989 .

[10]  S. Redner.  A guide to first-passage processes , 2001 .

[11]  N. Kampen,et al.  Stochastic processes in physics and chemistry , 1981 .

[12]  S. Havlin,et al.  Diffusion and Reactions in Fractals and Disordered Systems , 2000 .

[13]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[14]  Albert-László Barabási,et al.  Internet: Diameter of the World-Wide Web , 1999, Nature.

[15]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[16]  S. Redner,et al.  First-passage properties of the Erdos Renyi random graph , 2004, cond-mat/0410309.

[17]  Subhasis Banerjee,et al.  Reaction-Diffusion Processes on Random and Scale-Free Networks , 2004 .

[18]  K. Sneppen,et al.  Diffusion on complex networks: a way to probe their large-scale topological structures , 2003, cond-mat/0312476.

[19]  S. Havlin,et al.  Breakdown of the internet under intentional attack. , 2000, Physical review letters.