Trapping in complex networksA. 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
received 6 June 2008; accepted in final form 6 October 2008; published November 2008
published online 12 November 2008
We investigate the trapping problem in Erdős-Rényi (ER) and scale-free (SF) networks. We calculate the evolution of the particle density 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 , for longer times 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: 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 for all , where is the exponent of the degree distribution .
05.40.Fb - Random walks and Levy flights.
82.20.Wt - Computational modeling; simulation.
89.75.Da - Systems obeying scaling laws.
© EPLA 2008