2000/05/31 by A. D. Barbour, Barbour, A. D., Gesine Reinert +1
Physics and Astronomy · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #cond-mat.dis-nn
paper · pdf · doi:10.48550/arxiv.cond-mat/0006001
Corrected version; see also the journal ``Random Structures and Algorithms''; 30 pages, 1 figure, 1 style file
arxiv created 2004/04/30 · arxiv updated 2009/11/30
Small world models are networks consisting of many local links and fewer long range `shortcuts'. In this paper, we consider some particular instances, and rigorously investigate the distribution of their inter--point network distances. Our results are framed in terms of approximations, whose accuracy increases with the size of the network. We also give some insight into how the reduction in typical inter--point distances occasioned by the presence of shortcuts is related to the dimension of the underlying space.