We study static annihilation on complex networks, in which pairs of connected particles annihilate at a constant rate during time. Through a mean-field formalism, we compute the temporal evolution of the distribution of surviving sites with an arbitrary number of connections. This general formalism, which is exact for disordered networks, is applied to Kronecker, Erdös-Rényi (i.e., Poisson), and scale-free networks. We compare our theoretical results with extensive numerical simulations obtaining excellent agreement. Although the mean-field approach applies in an exact way neither to ordered lattices nor to small-world networks, it qualitatively describes the annihilation dynamics in such structures. Our results indicate that the higher the connectivity of a given network element, the faster it annihilates. This fact has dramatic consequences in scale-free networks, for which, once the "hubs" have been annihilated, the network disintegrates and only isolated sites are left.




United States. Defense Advanced Research Projects Agency
Dirección General de Asuntos del Personal Académico (DGAPA)
National Science Foundation (U.S.)

Keywords and Phrases

Numerical Analysis; Reaction-Diffusion Systems

Document Type

Article - Journal

Document Version

Final Version

File Type





© 2005 American Physical Society (APS), All rights reserved.

Publication Date

01 Jan 2005

Included in

Physics Commons