Small worlds

Details Small worlds Small worlds

2000-05-31

arxiv.org/abs/cond-mat/0006001v2

Physics

Condensed Matter

Disordered Systems and Neural Networks

Corrected version; see also the journal ``Random Structures and Algorithms''; 30 pages, 1 figure, 1 style file

Scientific paper

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.

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