%0 Journal Article %T Small-World Networks: Links with long-tailed distributions %A S. Jespersen %A A. Blumen %J Physics %D 2000 %I arXiv %R 10.1103/PhysRevE.62.6270 %X Small-world networks (SWN), obtained by randomly adding to a regular structure additional links (AL), are of current interest. In this article we explore (based on physical models) a new variant of SWN, in which the probability of realizing an AL depends on the chemical distance between the connected sites. We assume a power-law probability distribution and study random walkers on the network, focussing especially on their probability of being at the origin. We connect the results to L\'evy Flights, which follow from a mean field variant of our model. %U http://arxiv.org/abs/cond-mat/0009082v1