Small-world networks: Links with long-tailed distributions

S. Jespersen, A. Blumen
2000 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
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
more » ... hts, which follow from a mean field variant of our model.
doi:10.1103/physreve.62.6270 pmid:11101959 fatcat:vwstdzzmxfd4noxltllw7psedy