We investigate the trapping of random walkers on small-world networks (SWN’s), irregular graphs. We derive bounds for the survival probability ${\Phi }_n^{\mathrm{SWN}}$ and display its analysis through cumulant expansions. Computer simulations are performed for large SWNs. We show that in the limit of infinite sizes, trapping on SWNs is equivalent to trapping on a certain class of random trees, which are grown during the random walk.

• Received 21 May 2001

DOI:https://doi.org/10.1103/PhysRevE.64.066104