Discrete small world networks

TL;DR

This paper analyzes the distribution of shortest path lengths in discrete small world networks, providing approximations and comparisons to simpler models to better understand their structural properties.

Contribution

It introduces new approximations for the distribution of graph distances in discrete small world networks with random shortcuts, enhancing understanding of their structural characteristics.

Findings

Derived approximations for graph distance distribution

Compared discrete and continuous small world models

Enhanced understanding of network diameter and clustering

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.