Issue
EPL
Volume 84, Number 4, November 2008
Article Number 40008
Number of page(s) 6
Section General
DOI http://dx.doi.org/10.1209/0295-5075/84/40008
Published online 12 November 2008
EPL, 84 (2008) 40008
DOI: 10.1209/0295-5075/84/40008

Trapping in complex networks

A. Kittas1, S. Carmi2, 3, S. Havlin2 and P. Argyrakis1

1   Department of Physics, University of Thessaloniki - 54124 Thessaloniki, Greece, EU
2   Minerva Center & Department of Physics, Bar-Ilan University - 52900 Ramat Gan, Israel
3   Center for Polymer Studies, Boston University - Boston, MA 02215 USA

panos@physics.auth.gr

received 6 June 2008; accepted in final form 6 October 2008; published November 2008
published online 12 November 2008

Abstract
We investigate the trapping problem in Erdős-Rényi (ER) and scale-free (SF) networks. We calculate the evolution of the particle density $\rho (t)$ of random walkers in the presence of one or multiple traps with concentration c. We show using theory and simulations that in ER networks, while for short times $\rho (t)\propto {\rm exp}(-Act)$, for longer times $\rho (t)$ exhibits a more complex behavior, with explicit dependence on both the number of traps and the size of the network. In SF networks we reveal the significant impact of the trap's location: $\rho (t)$ is drastically different when a trap is placed on a random node compared to the case of the trap being on the node with the maximum connectivity. For the latter case we find $\rho(t)\propto{\rm exp}\left[-At/N^\frac{\gamma-2}{\gamma-1} \langle {k} \rangle \right] $ for all $\gamma > 2$, where $\gamma $ is the exponent of the degree distribution $P(k)\propto k^{- \gamma}$.

PACS
05.40.Fb - Random walks and Levy flights.
82.20.Wt - Computational modeling; simulation.
89.75.Da - Systems obeying scaling laws.

© EPLA 2008