# Discrete small world networks

Barbour, A D; Reinert, G (2006). Discrete small world networks. Electronic Journal of Probability, 11(47):1234-1283.

## Abstract

Small world models are networks consisting of many local links and fewer long range shortcuts', used to model networks with a high degree of local clustering but relatively small diameter. Here, we concern ourselves with the distribution of typical inter-point network distances. We establish approximations to the distribution of the graph distance in a discrete ring network with extra random links, and compare the results to those for simpler models, in which the extra links have zero length and the ring is continuous.

## Abstract

Small world models are networks consisting of many local links and fewer long range shortcuts', used to model networks with a high degree of local clustering but relatively small diameter. Here, we concern ourselves with the distribution of typical inter-point network distances. We establish approximations to the distribution of the graph distance in a discrete ring network with extra random links, and compare the results to those for simpler models, in which the extra links have zero length and the ring is continuous.

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