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
... hts, which follow from a mean field variant of our model.
S. Jespersen, A. Blumen. "Small-world networks: Links with long-tailed distributions." Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 62.5 (2000) 6270-6274