We investigate the trapping problem in Erdős-Rényi (ER) and scale-free (SF) networks. We calculate the evolution of the particle density ρ(t) of random walkers in the presence of one or multiple traps. We show using theory and simulations that in ER networks, while for short times ρ(t) scales exponentially with time, for longer times it 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: ρ(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 reveal the dependence of ρ(t) on γ, where γ is the exponent of the degree distribution. We also find that as opposed to ER networks, particles survive for longer times in denser SF networks. Finally, when the trap is placed in one of the network hubs, we find a new scaling with the system size. The average time before trapping decreases dramatically in comparison too random failure or to ER networks. This is true for all values of γ, suggesting that the equivalence of SF and ER networks for γ>4 does not exist for the trapping problem.
Check out the publication in EuroPhysics Letters.