  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.
