Small-World Networks: Links with long-tailed distributions

Details Small-World Networks: Links with long-tailed distributions Small-World Networks: Links with long-tailed distributions

2000-09-06

arxiv.org/abs/cond-mat/0009082v1

Physics

Condensed Matter

Statistical Mechanics

11 pages, 4 figures, to appear in Phys.Rev. E

Scientific paper

10.1103/PhysRevE.62.6270

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.

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