Diffusion-annihilation processes in complex networks

2004/07/31 by Michele Catanzaro, Marian Boguna, Marián Boguñá +2 · 2 citations
Mathematics · Physics and Astronomy · #Bounded function #Combinatorics #Complex Network Analysis Techniques #Complex network #Degree (music) #Degree distribution #Diffusion #Exponent #Geometry #Inverse #Mathematical analysis #Mathematics #Opinion Dynamics and Social Influence #Physics #Power law #Quantum mechanics #Scale-free network #Statistical physics #Statistics #Stochastic processes and statistical mechanics #cond-mat.stat-mech

paper · pdf · doi:10.1103/physreve.71.056104

9 pages, 5 EPS figures

arxiv created 2004/08/06 · openalex publication_date 2005/05/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We present a detailed analytical study of the A+A --> 0 diffusion-annihilation process in complex networks. By means of microscopic arguments, we derive a set of rate equations for the density of A particles in vertices of a given degree, valid for any generic degree distribution, and which we solve for uncorrelated networks. For homogeneous networks (with bounded fluctuations), we recover the standard mean-field solution, i.e., a particle density decreasing as the inverse of time. For heterogeneous (scale-free networks) in the infinite network size limit, we obtain instead a density decreasing as a power law, with an exponent depending on the degree distribution. We also analyze the role of finite size effects, showing that any finite scale-free network leads to the mean-field behavior, with a prefactor depending on the network size. We check our analytical predictions with extensive numerical simulations on homogeneous networks with Poisson degree distribution and scale-free networks with different degree exponents.

Citations

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