Absence of depletion zone effects for the trapping reaction in complex networks.

In the present work we examine in detail the formation of a depletion zone in the trapping reaction in networks, with a single perfect trap. We monitor the particle density rho(r) with respect to the distance r from the trap. We show using Monte Carlo simulations that the depletion zone is absent in regular, Erdos-Renyi (ER), and scale-free (SF) networks. The density profiles show significant differences for these cases. The particles are homogeneously distributed in regular and ER networks with the depletion effect appearing in very sparse ER networks. In SF networks we reveal the important role of the hubs, which due to their high random walk centrality are critical in the trapping reaction. In addition, the degree distribution plays a significant role in the distribution of the particles recovering the depletion zone formation for high gamma values. The mean connectivity of the network is found to play a significant role in both ER and SF networks.